1. Measurement and Computation of Molecular Potential Energy Surfaces Polik Research Group Hope College Department of Chemistry Holland, MI 49423

2. Measurement and Computation of Molecular Potential Energy Surfaces Jennica Skoug, David Gorno, & Eli Scheele Polik Research Group Hope College Department of Chemistry Holland, MI 49423

3. Outline Potential Energy Surfaces Dispersed Fluorescence Spectroscopy –Molecular Beam –Lasers –Monochromator Resonant Polyad Model –Harmonic and Anharmonic Terms –Vibrational State Mixing Computation of PES’s and Vibrational Levels

4. Potential Energy Surfaces A Potential Energy Surface (PES) describes how a molecule’s energy depends on geometry Chemical structure, properties, and reactivity can be calculated from the PES

5. Measuring PES’s & Vibrational States Measuring highly excited vibrational states allows characterization of the PES away from the equilibrium structure of the molecule

6. Molecular Beam for Sample Preparation A molecular beam cools the sample to 5K Molecules occupy the lowest quantum state and simplify the resulting spectrum

7. Lasers for Electronic Excitation Laser provide an intense monochromatic light source Lasers motes molecules to an excited electronic state

8. Monochromator for Detection A monchromator disperses molecular fluorescence E vibrational level = E laser – E fluoresence

9. Dispersed Fluorescence Spectrum 3 1 HFCO

10. Summary of Assignments MoleculePrevious #Current # Energy Range (cm -1 ) Year H 2 CO812790 - 12,5001996 D 2 CO72610 - 12,0001998 HFCO443820 - 22,5002002 H 2 CO  H 2 +COdissociation barrier  28,000 cm -1 HFCO  HF+COdissociation barrier  17,000 cm -1

11. Harmonic and Anharmonic Models A harmonic oscillator predicts equally spaced energy levels Anharmonic corrections shift vibrational energy levels as the PES widens Harmonic Energy Anharmonic Correction

12. Polyad Model Groups of vibrational states interacting through resonances are called polyads Resonances mix vibrational energy levels Energy levels are calculated from the Schrodinger Eqn 22652265 k 26,5  215164215164 k 26,5  52635263  k 44,66 224263224263 k 26,5  2142516221425162 k 26,5  425261425261  k 44,66 224461224461 k 26,5  214451214451

13. Diagonal Elements: Off-Diagonal Elements: Harmonic Energy Anharmonic Correction Resonant Interactions Matrix Form of Schrödinger Equation

14. H 2 CO Anharmonic Polyad Model Fits ParameterFit 1Fit 2Fit3Fit 4 ω1°ω1°2818.92812.32813.72817.4  ω6°ω6°1260.61254.81251.51251.9 x 11 -40.1-29.8-30.7-34.4  x 66 -5.2-2.8-2.1-2.2 k 26,5 148.6146.7138.6 k 36,5 129.3129.6135.1 k 11,55 140.5137.4129.3 k 44,66 21.623.3 k 25,35 18.5 Std Dev23.44.343.342.80

15. Model Fits to Experimental Data

16. Polyad Quantum Numbers H 2 CO D 2 CO HFCO k 1,44 N vib = v 2 +v 3 +v 5 ( ultimately destroyed ) k 44,66 N CO = v 2 ( remains good! ) k 36,5 N res = 2v 1 +2v 2 +v 3 +v 4 +2v 5 +v 6 ( remains good! ) k 2,66 N polyad = 2v 2 +v 6 others? v 1, v 3, v 4, v 5 may remain good k 36,5 N oop = v 4 ( destroyed by k 44,66 ) k 26,5 N vib = v 1 +v 4 +v 5 +v 6 ( destroyed by k 1,44 and k 1,66 ) k 11,55 N res = 2v 1 +v 2 +v 3 +v 4 +2v 5 +v 6 ( remains good! )

17. Polyad Quantum Numbers H 2 CO D 2 CO HCCH k 1,44 N vib = v 2 +v 3 +v 5 ( ultimately destroyed ) k 44,66 N CO = v 2 ( remains good! ) k 36,5 N res = 2v 1 +2v 2 +v 3 +v 4 +2v 5 +v 6 ( remains good! ) many N str = v 1 +v 2 +v 3 ( ultimately destroyed ) reson- N l = l 4 +l 5 ( ultimately destroyed ) ances N res = 5v 1 +3v 2 +5v 3 +v 4 +v 5 ( remains good! ) k 36,5 N oop = v 4 ( destroyed by k 44,66 ) k 26,5 N vib = v 1 +v 4 +v 5 +v 6 ( destroyed by k 1,44 and k 1,66 ) k 11,55 N res = 2v 1 +v 2 +v 3 +v 4 +2v 5 +v 6 ( remains good! )

18. Computation of PES’s The Potential Energy E can be represented by a Taylor series expansion of the geometry coordinates q i A quartic PES requires computation of many high- order force constants (partial derivatives) Force constants predict vibrational energy level shifts and mixing

19. Parallel Computing Force constants are computed as numerical derivatives, i.e., by calculating energies of displaced geometries PES calculation takes hours instead of weeks with parallel computing

20. Computation of PES and Vibrations

21. Conclusions DF spectroscopy is a powerful technique for measuring excited states (general, selective, sensitive) Resonances shift and mix vibrational states The anharmonic polyad model accounts for resonances and assigns highly mixed spectra ( , x, k) Polyad quantum numbers remain at high energy (N res always conserved) High level quartic PES calculations and polyad model accurately predict excited vibrational states

22. Acknowledgements H 2 CO Rychard Bouwens (UC Berkeley - Physics), Jon Hammerschmidt (U Minn - Chemistry), Martha Grzeskowiak (Mich St - Med School), Tineke Stegink (Netherlands - Industry), Patrick Yorba (Med School) D 2 CO Gregory Martin (Dow Chemical), Todd Chassee (U Mich - Med School), Tyson Friday (Industry) HFCO Katie Horsman (U Va - Chemistry), Karen Hahn (Med School), Ron Heemstra (Pfizer - Industry), Ben Ellingson (U Minn – Chemistry) Funding NSF, Beckman Foundation, ACS-PRF, Research Corporation, Wyckoff Chemical, Exxon, Warner-Lambert