Measurement and Computation of Molecular Potential Energy Surfaces

1
Measurement and Computation of Molecular
Potential Energy Surfaces

• Polik Research Group
• Hope College
• Department of Chemistry
• Holland, MI 49423

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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

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Outline

• Potential Energy Surfaces
• Dispersed Fluorescence Spectroscopy
• Molecular Beam
• Lasers
• Monochromator
• Resonant Polyad Model
• Harmonic and Anharmonic Terms
• Vibrational State Mixing
• Computation of PESs and Vibrational Levels

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Potential Energy Surfaces

• A Potential Energy Surface (PES) describes how a
  molecules energy depends on geometry
• Chemical structure, properties, and reactivity
  can be calculated from the PES

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Measuring PESs Vibrational States

• Measuring highly excited vibrational states
  allows characterization of the PES away from the
  equilibrium structure of the molecule

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Molecular Beam for Sample Preparation

• A molecular beam cools the sample to 5K
• Molecules occupy the lowest quantum state and
  simplify the resulting spectrum

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Lasers for Electronic Excitation

• Laser provide an intense monochromatic light
  source
• Lasers motes molecules to an excited electronic
  state

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Monochromator for Detection

• A monchromator disperses molecular fluorescence
• Evibrational level Elaser Efluoresence

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Dispersed Fluorescence Spectrum
31 HFCO
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Summary of Assignments
Molecule Previous Current Energy Range(cm-1) Year
H2CO 81 279 0 - 12,500 1996
D2CO 7 261 0 - 12,000 1998
HFCO 44 382 0 - 22,500 2002
H2COH2CO dissociation barrier 28,000
cm-1 HFCOHFCO dissociation barrier 17,000 cm-1
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Harmonic and Anharmonic Models

• A harmonic oscillator predicts equally spaced
  energy levels
• Anharmonic corrections shift vibrational energy
  levels as the PES widens

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Polyad Model
2265 k26,5 215164 k26,5 5263
? k44,66 ? k44,66 ? k44,66
224263 k26,5 21425162 k26,5 425261
? k44,66 ? k44,66
224461 k26,5 214451

• Groups of vibrational states interacting through
  resonances are called polyads
• Resonances mix vibrational energy levels
• Energy levels are calculated from the Schrodinger
  Eqn

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Matrix Form of Schrödinger Equation
Diagonal Elements Off-Diagonal Elements
HarmonicEnergy
AnharmonicCorrection
Resonant Interactions
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H2CO Anharmonic Polyad Model Fits
Parameter Fit 1 Fit 2 Fit3 Fit 4
?1 2818.9 2812.3 2813.7 2817.4
? ? ? ? ?
?6 1260.6 1254.8 1251.5 1251.9
x11 -40.1 -29.8 -30.7 -34.4
? ? ? ? ?
x66 -5.2 -2.8 -2.1 -2.2
k26,5 148.6 146.7 138.6
k36,5 129.3 129.6 135.1
k11,55 140.5 137.4 129.3
k44,66 21.6 23.3
k25,35 18.5
Std Dev 23.4 4.34 3.34 2.80
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Model Fits to Experimental Data
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Polyad Quantum Numbers

• H2CO
• D2CO
• HFCO

k36,5 Noop v4 (destroyed by
k44,66) k26,5 Nvib v1v4v5v6 (destroyed by
k1,44 and k1,66) k11,55 Nres 2v1v2v3v42v5v6
(remains good!)
k1,44 Nvib v2v3v5 (ultimately
destroyed) k44,66 NCO v2 (remains
good!) k36,5 Nres 2v12v2v3v42v5v6
(remains good!)
k2,66 Npolyad 2v2v6 others? v1, v3, v4, v5 may
remain good
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Polyad Quantum Numbers

• H2CO
• D2CO
• HCCH

k36,5 Noop v4 (destroyed by
k44,66) k26,5 Nvib v1v4v5v6 (destroyed by
k1,44 and k1,66) k11,55 Nres 2v1v2v3v42v5v6
(remains good!)
k1,44 Nvib v2v3v5 (ultimately
destroyed) k44,66 NCO v2 (remains
good!) k36,5 Nres 2v12v2v3v42v5v6
(remains good!)
many Nstr v1v2v3 (ultimately
destroyed) reson- Nl l4l5 (ultimately
destroyed) ances Nres 5v13v25v3v4v5
(remains good!)
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Computation of PESs

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

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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

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Computation of PES and Vibrations
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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 (w,
  x, k)
• Polyad quantum numbers remain at high energy
  (Nres always conserved)
• High level quartic PES calculations and polyad
  model accurately predict excited vibrational
  states

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Acknowledgements

• H2CO
• Rychard Bouwens (UC Berkeley - Physics), Jon
  Hammerschmidt (U Minn - Chemistry), Martha
  Grzeskowiak (Mich St - Med School), Tineke
  Stegink (Netherlands - Industry), Patrick Yorba
  (Med School)
• D2CO
• 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