Where Spectroscopy Meets Dynamics: High Resolution Studies of Radicals and Molecular Ions

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Where Spectroscopy Meets Dynamics High
Resolution Studies of Radicals and Molecular Ions

• Frontiers in Spectroscopy
• Department of Chemistry and The Ohio State
  University
• Columbus, OH
• January 17, 2007
• Work done at
• JILA/Department of Chemistry and Biochemistry
• National Institute for Standards and Technology
• University of Colorado
• Boulder, CO

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Thanks in advance to all Nesbitt group members
(and collaborators)!
Go Buckeyes!
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Big Picture Goals
Theory
Experiment

• Close interface between (maximally) rigorous
  theory and experiments on (maximally) simplified
  systems
• Þ Evolution/testing of fundamental paradigms

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Definitely not the goal
(i.e. questions welcome!)
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Todays Menu

• Overview of experimental ideas
• Slit jet spectroscopy
• High resolution absorption methods
• Discharges
• Applications to
• I. Radicals (e.g., methyl, ethyl, cyclopropyl)
• II. Molecular Ions (e.g., hydronium ion)
• Role of theory
• Summary

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Fridays Menu

• From Single Collisions to Single Molecules
• I) Molecular Splashes
• Quantum state-to-state collision dynamics at the
  gas-liquid interface probed with high
  resolution IR spectroscopy!
• II) Molecular Pretzels
• Watching biomolecular folding kinetics and
  dynamics at the single molecule level using
  laser induced fluorescence, time resolved single
  photon counting and confocal microscopy

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Experimental

• Beers Law detection (i.e., A Ns l)
• but with full v,J quantum resolution (Dn
  0.0001 cm-1)
• at the fundamental shot noise limit (10-6
  /Hz1/2)
• Universal, state-selective and surprisingly
  sensitive!

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Beers Law at 10-9 Torr !
300 mm
5 cm

• Absorbance N s l
• 5 cm slit x 20 fold multipass (x 100 enhancement
  in l)
• 1/r vs 1/r2 density drop off in slit (x 100
  enhancement in r)
• Sub-Doppler resolution by velocity collimation (x
  10 enhancement in s)
• Laser noise subtraction down to shot noise
  limit (lt .005 in 10 KHz)
• Þ Nmin 107 /cm3/q.s. sensitivities

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A Molecular Scale Picture
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Jet Cooled Radicals

• Clean synthesis of radicals by electron
  dissociative attachment to alkyl halides (RX e-
  R X-)
• High radical densities at slit orifice (1013
  -1015 /cm3)
• Simple high resolution spectroscopy at 5-20 K

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Supersonic Slit Discharges

• Negative discharge polarity
• Electrons flow upstream, heavy cations move
  downstream with the supersonic expansion
• Intense (1A), stable and confined discharges at
  500 Torr!
• Highly localized (1 mm) discharge ( 105 cm/s,
  1 ms transit time)

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Secondary Chemistry?(too little time!)

• R 3x1014 /cm3 (inside discharge)
• R R M products (3-body recombination)
• R R products (2-body reactions)
• t3-body (10-30cm6/s) (3x1014/cm3)(1019/cm3)-
  1
• 300 msec gtgt ttransit 1 ms
• t2-body (10-11cm3//sec) (3x1014/cm3)-1
  300 msec gtgt ttransit 1 ms
• Þ synthesize, jet-cool, and study highly
  reactive primary species in absence of secondary
  chemical reactions

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Concentration Modulation
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Microslit Injectors

• 200 mm holes
• Pulsed injection of secondary reagents into the
  slit expansion
• Control of chemistry in the post-discharge region

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In Action

• Gentle, efficient electron dissociative
  attachment, e- RX R X-
• Jet cooled radicals studied methyl, ethyl,
  allyl, cyclopropyl, chloromethyl, fluoromethyl,
  vinyl,

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A Typical Lab Scene

• Post docs and grad students eager for hot
  experimental tips from their research advisor

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So Why Should We Care About Radical Spectroscopy?

• Almost all chemistry occurs via trace levels of
  highly reactive radicalsneed to understand the
  key players to control the fundamental reaction
  dynamics!
• Spectroscopy provides detailed information on
  radical structures and energetics for precision
  benchmarking of high level theory
• Sensitive laser tools for probing reactions in
  complex mixtures (kinetics, combustion, etc)

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Systems Studied
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I. Methyl Radical

• Simplest prototype for cyclic open shell
  hydrocarbon ring
• Large amplitude out of plane bending motion
• Model system for spin density transfer
• Through-space vs. through bond spin
  interactions
• No dipole moment (i.e. no rotational spectrum)

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Jet Cooled CH3 Transitions

• Spectroscopy gets simple at low temperatures!
• CH3 jet cooled into lowest nuclear spin states
  (I3/2, I1/2)

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A Bonus at High Resolution

• Electron/nuclear spin (IS) hyperfine structure!
• Probe of spatial distribution of electron spin
  density in radicals

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CH3 Hyperfine Analysis

• H AF IS (Fermi contact, i.e. measure of
  electron spin density at H nucleus with respect
  to C nucleus)
• AF lt 0 ( -65.5(9) MHz)
• Implies radical spin density in CH3 changes sign
  between H and C nuclei!

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Simple Physical Picture (Spin Polarization)

• Direct confirmation of predicted spin
  polarization waves in CH3 radical

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II. Ethyl Radical

• Fundamental prototype for large amplitude QM in
  open shell systems
• Single vs (partial) double C-C bond character?
• Barriers to C-C internal rotation?
• Equilibrium geometry?
• Hyperconjugation effects?

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Torsion-Rotational Symmetries
(A Vibr. Ex. State)
(2,1)
Nuclear Spin Sym A A
E E Weight 12
4 6 2

• 3-fold CH3 axis Þ A/E states 2-fold CH2 axis Þ
  / states
• Þ 4 different nuclear spin symmetries A, A,
  E, E

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• At 10K jet temperatures Þ (relatively!) simple
  spectroscopy
• (First) precision structural information on ethyl
  radical
• C-C bond length shortening (partial 5 double
  bond character)

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At Higher Resolution

• Spectral fine structure due to coupled CH2
  bending and internal C-C bond rotation
• Complex intramolecular vibrational dynamics even
  in simple open shell radicals!

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Ab Initio Confirmation

• Strong 2D coupling between CH2 bend and internal
  rotation
• Breakdown of simple 1D rotation picture around
  C-C bond

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Physical Picture

• Hyperconjugation between CH2 p orbital and CH
  bond in CH3
• Pulls CH2 group away from planarity
• Large ( 1 kcal) barrier for 1D path
• Small ( 20 cm-1) barrier for 2D path
• Coupled bending and internal rotation

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What about the CH3 Vibrations?

• Weak hyperconjugation limit Þ like isolated CH3
• i) Lower frequency, sym CH stretch ( band)
• ii) Near-degenerate higher frequency asym CH
  stretches ( band(s))

• Strong hyperconjugation limit (not at all
  obvious!) one CH bond softens and breaks 3-fold
  equivalence
• i) Lone CH stretch (red shifted)
• ii) Widely separated pair of sym/asym CH
  stretches ( 102 cm-1)

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Observed CH3 Group Vibrations



124 cm-1
3000
2900

• More consistent with strong hyperconjugation
  effects

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Local Mode Coupling Model

• 3 harmonic CH oscillators with r dependent spring
  const
• kl(r)k0-Dksin2(r-2pl/3) (l0,1,2), kinetic
  coupling µ piGijpj
• Vibrationally non-adiabatic curve crossings
  clearly evident

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Physical Picture
H red shifted nCH H blue shifted nCH H normal
nCH

• Local CH stretch vibration rotates 3x faster
  than C-C bond !
• Strongly coupled CH stretch/CC rotor
  intramolecular energy flow

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III. Cyclopropyl Radical
D

• Simplest alkyl ring radical
• Tunneling dynamics?
• Prospects for chiral synthesis?
• Unimolecular ring-opening?
• Height of inversion barrier?

DH0 -22 kcal/mol
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Over the Top

• a-CH flopping between identical minima on
  global potential energy surface

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In-phase Antisymmetric CH2 Stretch
Nuclear spin statistics in the ground state (Ka
Kc) Symmetric level ? even odd 6
10 Asymmetric level ? even odd 10 6
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Lower Tunneling State Q-Branch

• First high resolution detection/structural
  information for cyclopropyl radical

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Tunneling Assignment

• Clear nuclear spin intensity alternation in KaKb
  (evenodd 610)
• Unambiguous assignment to transitions out of the
  ground state symmetric tunneling level

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Upper Tunneling State Spectra

• Two closely spaced cyclopropyl bands ground
  state combination differences agree to 15 MHz
• Nuclear spin statistics clearly consistent with
  upper tunneling state (asymmetric)
• Dark state IVR coupling in the excited
  vibrational manifold

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Boltzmann Tunneling Analysis

• Thermally equilibrated upper and lower tunneling
  state populations (high density slit vs pinhole
  expansions)
• Permits extraction of tunneling splitting
  (DEtun 3.2(3) cm-1) from Boltzmann analysis of
  upper/lower population ratios

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Extracting Tunneling Barriers

• High level CCSD(T) ab initio 1D PES along the
  a-CH inversion coordinate (AVnZ, nD,T,Q, CBS
  limit, ZPE included)

• Linearly scale barrier to match experiment Þ V0
  1115(35) cm-1
• Much larger barrier than previously
  anticipatedbut still too facile tunneling to
  allow stereospecific chemistry around radical
  center (k0 ? 2.01011 s-1)

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IV. Hydronium Ion

• Ubiquitous role in aqueous chemistry and biology
• Large amplitude QM tunneling in umbrella mode
• Benchmark test system for high level ab initio
  and full 6D quantum dynamics

Begemann, and Saykally, PRL 1983 Liu Oka, PRL
1985 Verhoeve and Dymanus, CPL 1989 Araki and
Saito, JCP 1998.
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Quiz Question Do Floppy Molecules Still Yield
High Resolution IR Spectra?

• Yes!
• HY EY still satisfied only for discrete
  energies
• but Y is delocalized over the potential energy
  surface

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Tunneling Dynamics in HnD3-nO Isotopomers

• ? Symmetry breaking from C3v to Cs (tunneling
  through a C2v trans state)
• makes transitions between all tunneling states
  allowed in HD2O and H2DO
• ? Can map out inversion barrier by systematic
  tuning of tunneling masses from H3O to H2DO
  to HD2O to D3O

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Rational Synthesis of Isotopomers

• H3 D2O H2 HD2O
• H3 HDO H2 H2DO
• (or D3 H2O D2 H2DO)

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Sample HD2O Data
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Global View HD2O

• Large tunneling splittings
• DEtun 27.032 cm-1
• DEtun 17.761 cm-1
• Dramatic decrease in tunneling splittings (DEtun)
  with increasing OH stretch quanta (vOH)

nss
naa
nas
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Thermal Tunneling Analysis

• From direct spectroscopic measurement..
• DEtun 27.0318(72) cm-1
• From thermal Boltzmann analysis
• DEtun 26.5 1.5 cm-1
• Vibrational equilibration in slit jet expansions
• (i.e. Tvib Trot)
• Confirms previous analysis of cyclopropyl
  tunneling barrier height

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Completing the isotopomer series H2DO

• No isotopic symmetry breaking in asymmetric OH
  stretch (i.e. pure B-type)
• Symmetry breaking in the symmetric OH stretch
  (i.e. hybrid A- and C-type)
• Need to observe 5 out of 6 vibl bands to get any
  tunneling splittings in H2DO

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Sample H2DO Data

• 5 out of 6 possible tunneling bands observed
• tunneling splittings in ground, sym and asym OH
  stretch states

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Experiment vs Theory?

• Excellent agreement with theory
• with large decrease in tunneling splittings
  (i.e. increase in barrier height) with OH/OD
  vibl excitation

a Liu Oka, PRL 1985 b Tang Oka, JMS 1999 c
Araki Saito, JCP 1998 d Petek et al. JCP
1989. All units in cm-1.
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Simple Physical Picture

• sp2
• (stiffer OH)

• sp3
• (softer OH)

• sp3
• (softer OH)

• sp3 vs sp2 competition Stiffening of OH
  stretch
• Increase in vibrationally adiabatic vOH1
  energies at planar configurations
• results in a strong decrease in tunneling rate
  with OH vibl excitation

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Extracting Tunneling Barriers From Spectra

• Geometry optimization and frequencies at
  CCSD(T)/AVTZ along the tunneling path
• Complete basis set extrapolation from CCSD(T),
  AVnZ (nD,T,Q)
• ZPE corrections for all other vibrational modes
• Exact reduced mass G-matrix coupling (Rush and
  Wiberg)
• Tunneling eigenvalues/ eigenfunctions on scaled
  CCSD(T) PES to extract full 6D experimental
  barrier height

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An Experimental Value

• Etun 652.9(6) cm-1 tunneling barrier for H3O
  isotopomers
• Near quantitative agreement with benchmark ab
  initio calculations of Halonen et al (650 cm-1)

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WBK Tunneling Analysis

• Powerful semiclassical method for analytic
  solution to 1-D S. E.
• Classical momentum p(q) 2m(q)(E-V(q))1/2
• Classical action under the tunneling barrier
• S òdq p(q) òdq2m(q)(V(q)-E)1/2
• Semiclassical WKB analysis predicts DEtun/hwinv
  (1/p) exp(-S/h)
• Þ Tunneling splitting should decrease
  exponentially with action under the barrier

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WKB Interpolation

Begemann, Saykally, Oka, Dymanus,
(Full 6D Theory) Bowman et al Halonen et al

• DV0 (Halonen Bowman WKB interpolation)
  653.0(7) cm-1
• In quantitative agreement with DV0 (expt)
  652.9(6) cm-1

Petek, Saykally, Moore, Saito,

• WKB analysis DEtun/hwinv (1/p) exp(-S/h)
• S (action) òdq2m(q)(V(q)-E)1/2
• Þ lnDEtun A b m(q0)DV01/2

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Summary

• High resolution IR studies for hydronium ion
• Precision tunneling splittings for umbrella
  inversion barrier systematically sampled by
  isotopic substitution (HnD3-nO)
• High level ab initio CCSD(T) CBS surfaces
• plus exact reduced masses (m(q)) as function of
  inversion
• yields experimental value for 6D tunneling
  barrier
• in excellent agreement with full 6D surface
  calculations (Bowman, Halonen, et al)
• Confirmation of barrier height by semiclassical
  WKB interpolation of full 6D tunneling calcs

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The CH5 Challenge.

• Highly delocalized fluxional quantum dynamics
• Complete breakdown of conventional
  vibration-rotation separation
• Spectroscopy without structure

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Molecular Splashes

• Quantum state resolved collisional energy
  transfer and reaction dynamics at the gas-liquid
  interface

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Molecular Pretzels

• Fluorescence resonant energy transfer (FRET)
  studies of RNA folding kinetics at the single
  molecule level

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Acknowledgement
Feng Dong (Los Gatos) Melanie Roberts Richard
Walters Scott Davis (Vescent) Dairene Uy
(Ford) Joel Bowman Mark Child Lauri Halonen
NSF AFOSR
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Scott Davis (Vescent Photonics)Thomas Haeber
(Duesseldorf)Feng Dong (Los gatos Research)Erin
Whitney (NREL) Dairene Uy (Ford Research) Mike
Deskevich Melanie Roberts Richard
WaltersNSFDOE AFOSR
(picture taken during a Nesbitt group raft trip
investigating large water clusters near Boulder!)
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Thanks to OSU Colleagues and Collaborators!
(always demonstrating the elegant dance between
theory and experiment!)