1. Structure and tunneling dynamics of gauche-1,3-butadiene
Bryan Changala1, Joshua Baraban2,3, Marie-Aline Martin-Drumel4,5, Sandra Eibenberger6, David Patterson6, John Stanton7, Barney Ellison3, and Michael McCarthy4
1JILA & Department of Physics, University of Colorado Boulder 2Department of Chemistry, Ben-Gurion University 3Department of Chemistry and Biochemistry, University of Colorado Boulder 4Harvard-Smithsonian Center for Astrophysics, Harvard University 5Institut des Sciences Moléculaires d’Orsay, CNRS, Univ. Paris-Sud, Université Paris-Saclay 6Department of Physics, Harvard University 7Department of Chemistry, University of Florida

2. Diels-Alder cycloaddition
Butadiene: a prototypical conjugated π-system
Diels-Alder cycloaddition
trans isomer more stable than “cis”
“cis”  gauche

3. FTMW spectrometers & gauche production McCarthy and Patterson labs
Cavity enhanced FTMW w/ supersonic expansion
1 kV electric discharge
5 kHz resolution
Chirped-pulse FTMW in cryogenic buffer gas cell
Heated inlet (230°C)
80 kHz resolution 1 2
10K He buffer gas cell
inlet

4. Rotational spectroscopy of gauche-butadiene
Goals:
1. Equilibrium gauche structure:
Beq = B0 - ΔB0
2. Tunneling splitting and its effects on the ground state rotational structure

5. Ab initio ro-vibrational corrections and tunneling splitting
Accurate ΔB0 and tunneling predictions require full dimensional, anharmonic rovibrational calculations.
Problem 1: C4H6 is relatively large. Numerically exact variational nuclear motion calculations would be prohibitively expensive.
Problem 2: Standard approximate methods like VPT2 are efficient, but do not treat tunneling systems.
Our approach: a VMP2-based rovibrational method for non-rigid molecules

6. Rotational VMP2 (see talk TD02)
PBC & J.H. Baraban, J. Chem. Phys. 145, (2016)
1. Find optimal Hartree product vibrational wavefunction in terms of 3N-6 curvilinear internal vibrational coordinates qi
Energy
Target states not isolated
Account for remaining (weak) interactions perturbatively (via contact/Van Vleck transformation)
2. Treat correlation between vibrational coordinates and rotation-vibration interactions up to 2nd order in perturbation theory
Treat subset of states non-perturbatively 0+ 0-
The internal vibrational coordinate system is critical user input!
What is the “correct” choice?

7. Rotational VMP2 with an isomerization path coordinate system

8. Rotational VMP2 with an isomerization path coordinate system
“Steepest descent” reaction path
-34o 0o
34o

9. gauche rotational constants
Parameter
Expt.
VMP2
VMP2 + Beq corrections
v = 0+
A0 / MHz
21223
21128
21219 B0
5671
5614
5669 C0
4577
4541
4573
v = 0- A0
21232
21135
21226
5667
5610
5665
4581
4544
4576
Average Error/MHz
63 (0.8%)
4 (0.05%)
Beq = B0 - ΔB0 
Non-planar

10. gauche structural features
C=C—C=C conjugation (favors planarity) vs. steric interactions of terminal H’s (non-planarity)
Semi-empirical equilibrium structure (rse)
1Craig, Groner, and McKean, J. Phys. Chem. A 110, 7461 (2006)
2This work, partial structure

11. gauche-gauche tunneling splitting
is a vibrationally forbidden transition!
How can we measure splitting?
Via perturbations!
v=0-
v=0+
v=0-
v=0+
Parameter
Expt.
VMP2
Tunneling splitting / cm-1
0.55
0.58
JaJc+JcJa interaction / MHz
23.4
23.3
For the d6
isotopologue:
 30 ps tunneling time

12. Conclusions
gauche-butadiene has a significantly non-planar structure and readily tunnels between gauche enantiomers
Curvilinear rotational VMP2 successfully treats the large amplitude nuclear motion and rotation-vibration interactions
A complete structure fit requires additional isotope substitution measurements … in progress!
Thanks for you attention!
Acknowledgements
Expt. assistance: E.S. Palmer, P. Antonucci, G. T. Buckingham
Funding: NSF, Welch Foundation, Austrian Science Fund

13. Summary of measured constants

14. 1D torsional levels

15. Outline
Experimental: Fourier transform microwave (FTMW) spectrometers; production of gauche-butadiene
Spectroscopy of tunneling gauche-butadiene
Structure and dynamics: theory & expt.
Semi-empirical gauche structure
Determination of tunneling frequency 1 2 3