Connecting Chemical Dynamics in Gases and Liquids

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Connecting Chemical Dynamics in Gases and Liquids
Mausumi Goswami
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Broad objective
An understanding and comparison of chemical
dynamics in gases and liquids is essential to
understand the reactivity of isolated molecules
in a complex medium
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• To undergo a chemical reaction, the reactants
  should have enough energy along the reaction
  co-ordinate.
• In solution, the relative rate for coupling of
  energy into the reaction co-ordinate compared to
  that for energy transfer to the solvent and to
  other un-reactive modes of the solute may dictate
  the rates, pathway and the efficiencies of the
  reactions.

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Representative example

• Bi-molecular reaction in which CN- abstracts a
  hydrogen from CHCl3 The reaction rate and
  product HCN vibrational state distributions are
  very different in solution

• Photodissociation of s-tetrazine into HCN and N2
  with visible light has a unit quantum yield for
  the isolated molecule and nearly zero-efficiency
  in solution

Need for the detailed understanding/comparison of
vibrational relaxation processes in gases and
solutions
Annu. Rev. Phys. Chem, 45, 519, 1994
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How the vibrational energy distribution dynamics
in the gas phase will be modified by the solvent?
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Plan of Talk

• Vibrational energy relaxation in isolated
  molecule
• Vibrational energy relaxation in the solvent
• Characteristic signature of the dynamics in
  frequency-domain and time-domain
• Vibrational relaxation dynamics of terminal
  acetylene
• Conclusion

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Vibrational Energy Redistribution in an isolated
molecule

Intramolecular vibrational energy redistribution
(IVR) Timescale 10-12s
Distribution of energy in different vibrational
modes in the molecule governed by the intrinsic
coupling in the molecule

• Total vibrational energy of the molecule is
  conserved

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Vibrational Energy Relaxation in solution

Total
Relaxation in solution
Two components
Intramolecular process

• Inherent IVR
• Solvent mediated IVR

Intermolecular
(VER)
Vibrational energy relaxation in the presence of
the solvent
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Dependence of interplay between the
intramolecular and the solvation dynamics

• Small molecule and the large molecule limit
  number of vibrational modes
• Level of excitation

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• Vibrational relaxation in liquid is not
  necessarily ultrafast. The range varies from
  sub-picosecond to second!!
• Weakly interacting system
• HCl in Xe and liquid N2 relax on micosecond
  and second timescale.
• 800 ps for W(CO)6 in CCl4
• Strongly interacting system
• Ions in polar solvents has relaxation time
  less than 10 ps.
  

Annu. Rev. Phys. Chem, 45, 519, 1994
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Techniques used
Liquid phase
Gas phase

• TIME DOMAIN

• FREQUENCY DOMAIN
• TIME DOMAIN

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IVR Three Tier Model
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Manifestation of IVR In spectra
Time-resolved
Frequency resolved
J. Phys. Chem. 85, 3592, 1985
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Vibrational Dynamics of Terminal Acetylenes
J. Phys. Chem. A, 108, 1348, 2004 J. Phys. Chem
A, 108, 1365, 2004
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Systems
MB
Propyne
Methylbutyne
3FB
Propargyl Fluoride
3-fluorobutyne
4FB
4-fluorobutyne
Propargyl Chloride
TBA
1-butyne
tert-butylacetylene
PCl
trimethylsilylacetylene
Methylbutenyne
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Features of terminal acetylene

• Solvent-induced relaxation pathway is dominated
  by the energy transfer to modes which are in
  close proximity of the solvent

• Normal-mode frequencies that are proximate to
  acetylenic C-H stretch are almost constant for
  all systems under study.

http//faculty.virginia.edu/bpate-lab

• The acetylenic chromophore serves to keep the
  moving atom 3.7Å from the rest of the molecule.

• Energy relaxation by the solvent is expected to
  be same for all the molecules in this study-
  trends can be established in this series

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• Solvent systems chosen
• CCl4, CHCl3,CDCl3, CH2Cl2 and CCl3CN

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Method Picosecond Transient Absorption
Spectroscopy

• To monitor the lifetime of the C-H stretch
  excited state

V 2
?C-H 3330 cm-1(Gas phase)
Probe
?C-H 3310 cm-1(solution)
V 1
Energy
Pump
?C-H
V 0
Time
A decay of the absorption profile will be obtained
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Experimental Set-up
http//faculty.virginia.edu/bpate-lab
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Decay profile
0 300
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Result for the lifetime measurement in the gas
phase
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Propyne, Propargyl chloride, Propargyl fluoride
calculated density of states at 3330 cm-1 is less
than the IVR threshold

• IVR or collisional relaxation?!
• Assumed to be IVR

• ?1 is related to IVR
• ?2 is related to collisional relaxation ( Mean
  collision time 200 ps)

Absorption change (OD)

• ? is related to IVR

Time (ps)
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t0
t 1/e time of the IVR decay
longer time
Inhomogeneity in the spectra
Rotationally mediated interaction
Homogeneous decay
Anharmonic interaction causes the decay

• The Q branch intensity is dominated by the JK
  line in the spectra
• The P/R branch intensity is dominated by the k0
  line in the spectra

Except Propyne all the molecules show homogeneous
decay profile
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Lifetimes (ps) of the Relaxation Processes in
Dilute Solutions at Room Temperarture
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All the molecules in the solution shows single
exponential decay of IVR rate whereas in the gas
phase five molecules show bi-exponential decay
except TMSA and the molecules which has state
density less than the IVR threshold
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Interplay of IVR and VER dynamics comparison of
the solution rates(CCl4) and the initial
relaxation rates in gases
Slope 1.02(0.04) Intercept (67(22) ps)-1

• IVR contribution to the total relaxation is same
  as gas phase
• Solvent rate contribution to the total relaxation
  rate is very less

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Rate Model for Population Relaxation in Solution
No solvent-mediated IVR
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• A single VER rate describes the solvent
  contribution to the total relaxation rate for all
  the terminal acetylene

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Vibrational State density dependence of the Rate
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Rate model is found to hold good in all solvents
CCl4 data

• VER rate is found to be solvent dependent

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What can be the possible origin of bi-exponential
decay in gas phase?

• Different set of population is undergoing IVR in
  different time-scale
• All thermally populated levels are undergoing
  hierarchical IVR which are happening at two
  different time scale

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FTIR spectra for Propyne and Propargyl Fluoride
in acetylenic CC stretch region
7.7 cm-1
Absorbance
4.3 cm-1
cm-1
Sequence band collapse is not observed in the
solution
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Consideration of the play of hierarchical IVR
process in terminal acetylene to explain the
bi-exponential decay in gas phase

• Hierarchy of anharmonic interaction with the
  vibrational bath

IVR on distinct timescale has been observed where
C-H stretch is near resonant with the overtone of
the C-H bend eg Benzene
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Tier model mechanism for terminal acetylene
Random matrix calculation
Total energy range in the calculation is 25
cm-1 Number of first-tier state 19 (0.76
states/cm-1) Number of second-tier states 2000
(80 states/cm-1)
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Calculations have been done in two steps
Step 1 Calculation without the second tier of
states
Initial decay rate to the 1st tier as a
single-exponential decay

• Decay rate for the initial relaxation process
• W root-mean-squared interaction matrix element
• ? Density of the first-tier states

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Step 2 Calculation including the second tier of
states
Overall decay profile reflects bi-exponential
pattern
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Experimental Verification of the Tier-model
mechanism

• Probing at -40 cm-1 below the fundamental
  frequency of C-H stretch frequency

(1,2)
-40 cm-1 from the fundamental C-H stretch
frequency
Population Relaxation
V 1
?C-H
V 0
(0,2)
Bending overtone state
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• Bleach Recovery Experiment Probing at the v 0-1
  frequency

Information about the total relaxation of the
full population
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Tier Model
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Dynamics of the population decay calculated using
the Random Matrix Model
Intermediate bending C-H overtone states
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Gas phase and Solution phase (CCl4) spectra for
TBA (tert-butylacetylene)
?1 5.9ps ?2 39ps
?1 7.8ps ?2 30ps
Absorption change (OD)
Absorption change (OD)
No fall!
? 6.1ps
Time (ps)
Gas-phase
CCl4
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• The amplitude of the bleach recovery signal
  will be having two components

• Bi-exponential SEP (Stimulated Emission Pumping)
  component

• Single exponential recovery signal

• Slow component of the bleach recovery signal is
  giving the information about the final state
  relaxation

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Nature of the absorption spectrum in the gas
phase (TBA)
-40 cm-1 from the fundamental frquency
Absorption change (OD)

• Constant absorption cross-section observed at -40
  cm-1 from fundamental frequency

Explains the reason for not seeing the fall in
the absorption spectrum
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Is the rate model valid for the slower step IVR
also?
Slope0.87(0.15) Intercept (81(29)ps)-1

• The purely intramolecular timescale is unaffected
  in the solvent
• Constant VER rate is contributing to the total
  fall rate in the solution

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Does solvent influence the dynamics?

• In gas-phase the initial redistribution process
  removes only 30-50 of the total population

• Observation of the single-exponential in solution
  indicates a complete population relaxation

YES
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• The relatively low amplitude of the initial decay
  in the gas phase is caused by the coherent energy
  flow back to the C-H stretch excited state.
• Solvent can cause the damping of the coherent
  intramolecular oscillation and hence increasing
  the extent of the population relaxation.

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Comparison of the bleach-recovery signal in the
gas phase and the solution phase

• Return to baseline in the solution phase signal

Gas phase
Solution phase
Energy in the low frequency wag modes (150-350
cm-1) is rapidly cooled by the solvent
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Comparison of VER and IVR for both the steps of
relaxation for five molecules showing
bi-exponential decay in the gas phase
IVR contribution is dominating in the solution
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Conclusion

• The intramolecular relaxation rate in the gas
  phase and solution phase is the same for the
  series of molecules in the study.
• The extent of the population relaxation has been
  modified as observed in the single-exponential
  decay profile in the solution.
• Decomposition of the total relaxation rate in the
  solution is likely to be due to weak
  solute-solvent interaction that do not
  significantly perturb the state structure of a
  molecule.

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Thanks for your attention
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Scatter Plots
Measurement uncertainty is 1x 1010 s-1
Calculated VER rate(1010 s-1)
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Comparison of the 1st and 2nd VER rates for
different solvents
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Conclusion

• IVR timescale is significantly faster than VER
  timescale
• The direct correlation of the total relaxation
  rate in dilute solution with the isolated
  molecule rate for both stages of the IVR process
  shows that the solvent effect makes a simple
  additive contribution to the relaxation process.
• Pico-second transition absorption spectroscopy
  applied to gas phase and solution phase terminal
  acetylene provides an example of the direct
  comparison of the IVR rate in gases and solution

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Spectrum for methylbutenyne
A coherent oscillation having a time-constant of
2.8 ps has been observed
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Consideration of the 1st possibility

• Frequencies of the in-plane and out-of-plane
  R-CC bending (wag) is 200-300 cm-1.
• At room-temperature, the relative population of
  the vibrational states with v1 and v0 in these
  modes is calculated to be 12

The bi-exponential decay in the gas phase could
be originating from the population in the states
having v0 and v1 in the wag mode.
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• In this model, the single exponential rate in the
  solution would arise from the very fast
  solvent-induced energy exchange between the
  states with v0 and v1 of the wag

• Several solution rate measurement shows a decay
  time of less than 10 ps the
  exchange mechanism timescale should be 1-5 ps

Collapse in any sequence band structure generated
by the wag
??? 1
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FTIR spectra for Propyne and Propargyl Fluoride
in acetylenic CC stretch region
7.7 cm-1
Absorbance
4.3 cm-1
cm-1
Sequence band collapse is not observed in the
solution
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Similar behaviour has been observed for all the
other solvents
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Correlation among the relaxation rate for all the
terminal acetylene in CCl4
C-H stretch rate (1011 s-1)
Bleach recovery slow rate(1011 s-1)