Silver NyamboDepartment of Chemistry, Marquette University,

Wisconsin

Towards a global picture of spin-orbit coupling in the halocarbenes

June 22 2012

Electronic structure of carbenes

• Carbenes contain a divalent carbon and feature low-lying singlet and triplet

states that differ greatly in reactivity

• A central goal in carbene chemistry has been to experimentally determine

and theoretically predict the magnitude of the singlet-triplet gap, and probe

spin orbit coupling between the singlet and triplet states

Studied by Merer and Travis, Lineberger, Harmony, Hirota, Sears, Chang, Kable, Reid, …

Mono-halocarbenes (:CHX)

:CHF :CHCl :CHBr :CHIS0

T1

S1

0

4000

8000

12000

16000

20000

Ene

rgy

in c

m-1 24000

28000S2

3

SVL Emission SpectroscopyE

nerg

y

S0

S1

T1

Bond angle supplement

Camera

Diffraction grating

time

Inte

nsity

Gate

4

Triplet levels as observed in SVL emission spectra

2000 2100 2200 2300

Cou

nts

red shift in cm -1

a(0,0,0)~

CHCl CDBr

5

CHI and CDI

Here we were originally unable to assign many of the observed levels in our SVL emission spectra

0 500 1000 1500 2000 2500 3000

0 500 1000 1500 2000 2500 3000

Red shift in cm-1

213

n

2n

0 1 3

n

1

0 1 2 3 4 5

a 00

~

• Bending states are severely

perturbed, with shift of

100 cm-1 for fundamental

• Putative triplet origin is

observed at 1407 cm-1

•In CDI, triplet origin is

observed near 1285 cm-1

6

Developing a global picture of spin-orbit coupling

Set up H matrix diagonalize least squares fit to observed levels

HSO

HSO

Singlet levels(Dunham Expansion)

Triplet levels(Dunham Expansion)

7

What about HSO?

Even for the smallest data set, we need > 250 spin-orbit matrix elements. How can we determine these?

Assume:

The vibrational overlaps are calculated from theoretical data (vibrational frequencies and l-matrix elements) at a benchmarked level of theory, using PGOPHER

Fit parameters: harmonic frequencies of S0 and T1, limited set of anharmonic parameters, HSO, and T00 (S0-T1)

8

Isn’t this a severe assumption?

We assume that the spin-orbit coupling is independent of nuclearcoordinates:

•Support for this comes in previous studies of CH2 by McKellar et al. where spin-orbit coupling varied by less than 20% over a broad range of bond angles (CALCS – Richard Dawes)

•As we expect, the largest vibrational overlaps are for levels containing bending excitation

9

Results: CHI and CDI

Data for the two isotopomers were fit with a common HSO: (cm-1)

10

Results: Vibrational Frequencies (cm-¹)

Species Mode Fit frequency Calculated frequencya

CHI (S0)

C-H stretch … 2896.5

Bend 1056(5) 1050.0

C-I stretch 574(4) 587.8

CHI (T1)

C-H stretch … 3131.8

Bend 805(20) 799.0

C-I stretch 616(15) 642.9

CDI (S0)

C-D stretch 2061(10)6 2121.0

Bend 793(12) 775.0

C-I stretch 565(6) 574.0

CDI (T1)

C-D stretch … 2314.8

C-I stretch 640(29) 648.0

Bend 562(13) 576.0

a Unscaled, B3LYP/Sadlej-pVTZ level. bAnharmonic value. 11

Energy Levels: CHI

Eigenvectors quantify the presence of strong mixing:

S0(0,0,3)

S0(0,1,1)Ψ=0.82ΨSo(0,1,1)+0.33ΨT1(0,0,0)+…

Ψ=0.98ΨSo(0,0,3)+..

Calc singlet levels Obs Calc triplet levels

12

Results for CHBr/CDBr

• CHBr: a fit to 36 levels yielded a Mean Absolute Difference (MAD) of 3.8 cm-1, improved from 16 cm-1 for a Dunham fit without spin-orbit coupling.

• CDBr: 40 levels were fit to MAD of 3.2 cm-1

• CH35Cl: a combination of SVL emission and SEP data including 53 levels were fit, with an MAD of 3.0 cm-1, representing a factor of two improvement from a simple Dunham fit

13

Comparison of derived spin-orbit coupling constants with those of the bare halogen atoms:

Spin-orbit coupling constants

CHI

CHBr

CHCl

(cm-1)

(cm

-1)

Slope = 0.142(1)

Halogen atom X aSpin Orbit Coupling Constant, Xso cm-1

Spin Orbit Coupling Constant, CHXso cm-1

I 5069 731

Br 2460 355

Cl 587 81

F 269 -

aHandbook of photochemistry, 3rd edition 14

Summary

• Carbenes are important reactive intermediates that display complicated spectroscopy and dynamics

• Using SVL emission and SEP spectroscopy, we have probed the singlet-triplet gap and spin-orbit coupling between S0 and T1

• In this talk, we used a global analysis to fit the observed data – in all cases to within experimental error

• The derived spin-orbit coupling constants show a good correlation with those of the halogen atom

• New values for the singlet-triplet gaps are obtained (not discussed here)

15

Acknowledgements

Advisor: Scott A. Reid

People:Chong TaoCalvin MukarakateScott KableTim SchmidtRichard DawesGeorge BacskayRichard JudgeWill PolikTrevor SearsEric Brown

Funding:National Science Foundation