Spectroscopic Observation of Dynamical Processes
Spectroscopy of reversible reactions and processes
The lineshape of the resonances depends on the life-time of the molecular species that is on the rate of forward and backward reactions
1
Spectroscopic Observation of Dynamical Processes
A unique tool for investigating dynamic processes without perturbing the system
NMR spectroscopy UV-VIS spectroscopy IR spectroscopy (EPR spectroscopy)
2
Spectroscopic Observation of Dynamical Processes
Irreversible reactions:
For slow reactions (rate constants for the reactions are 10"6 to 10"3 s1): changes in concentration of products and/or reactants versus time are monitored. The variable temperature study allows determination of activation enthalpy and entropy.
For fast reactions:
titration with the addition of the aliquots of one edduct to the another edduct. The increase in the products and decrease in edduct concentration could be seen from the spectra.
NMR spectroscopy, UV-VIS spectroscopy, IR spectroscopy
3
Timescale of Chemical Processes
frequen differen
is timescale
I KB? MM J
termolecular
oce
tocesses (nuclei or lectron movement
In
tramolecular elec
oveme
Chemical Exchange
NMR time scale:  ms to |Lis
Reversible processes Activation energies 20 — 100 kj mol~
Stable isomers at room temperature AG* > 100 -120 kj mol"1
Methods:
• Band shape analysis for fast exch. 20 - 80 kj mol"1
• Polarization transfer for slow exch. 80 - 100 kj mol"1
Temperatures -150 / +150 °C
Reaction Coordinate
6
ility
A
1-kC,
N
N
"N "N
CH3
CH3
A G* = A H* - T AS*
Possible separation at r.t
Direct equilibration
160 120
Flash photolysis
MW
NMR
ESR
80 40 0
A G* kJ mol1
Bond Energies
Theory of Activated Complex
A (g) + B (g) u [ActC]*     P(g) + Q(g)
Equlibrium constant of activated complex K* = [ActC]* / [A] [B]
Rate = k, [ActC]* = k, K* [A] [B]
k3 = t f = t kBT / h
t = transmission factor (=1) f = frequency of ActC decomp.
Rate = (t kBT / h) Ki [A] [B]
k = (t kBT / h) K*
AG * = - RT In K*
AG* = AH* -T AS*
Eyring Equation
Rate = (t kBT / h) K* [A] [B]
k = (t kRT / h) K*
t = transmission factor = 1
use:    AG * = - RT In K*
AG * = AH* - T AS*    Activation Parameters
k=tkuLK,__ h
tk T
\nk = \n-^-
tkbt
f
In* t
= ln
h tk
B
h
ag* rt
ag*
exp
v
-AG;
rt
j
_ tkbt ~~h~
exp
v
-ah rt
exp
v
as; r
= ln
tk0t   ah* as
h
rt
+
r
h rt
= ln^
h
ah* as* --h
rt
r
cs
|Energy change [kJ/mol]
0-120 kJ/mol
AS approx. +200 J/mol K
o........o = o
o
coordination bond molecular bond hydrogen bond
for AH = 60 kJ/mol
T = 300 K, AG = AH - TAS = 60 kJ/mol - 300 K x 200 J/mol K = 0 kJ/mol T = 200 K, AG = AH - TAS = 60 kJ/mol - 200 K x 200 J/mol K = 20 kJ/mol
AG = -RTInK
K=l,
K = 6x10-6,
T = 300 K T = 200 K
Energy change [kJ/mol]
coordination, molecular or hydrogen bonds
edducts       «        " products
for AG* = 60 kJ/mol
AG* = RT[23.76 -ln(k/T)]
k = 600 s-1 T = 300 K k = 0.0009 s1 T = 200K
Chemical Equivalence by Interconversion
Intramolecular exchange
■ Tautomeric Interconversion (Keto-Enol)
■ Restricted Rotation
■ Ring Interconversion
■ Ring whizzing
■ Conformational equilibria
Intermolecular exchange
■ Binding of small molecules to macromolecules
■ Protonation/deprotonation equilibria
■ Isotope exchange processes
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Types of Chemical Exchange
Dynamical processes
change (equilibrium constant, rate constant) with temperature Intermolecular processes
• Chemical reactions with formation of covalent bond: irreversible or reversible
• Formation of coordination bond: reversible
• Association of molecules, hydrogen bonding,
solvation of ions and molecules: reversible
Intramolecular processes: reversible
• Fluxionality is the conversion between non-distinguishable species
AG°= 0
Isomerization is the conversion between different species (keto/enol tautomerism)
AG°^ 0
Chemical Exchange in NMR
Magnetic site exchange •Two-site •Multiple-site
•Bond breaking
•Internal hindered rotation
Two classes of exchange processes:
•Mutual/degenerate exchange,
Fluxionality, topomerization, AG°= 0
•Non-mutual/nondegenerate exchange, Isomerization, AG°^ 0
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Mutual/Degenerate Exchange
Only one distinquishable molecule (at a low temperature) Fluxional molecules, topomerization AG°= 0
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Fluxional Molecules
Bridging — terminal exchange
■
Inversion of bicyclo [1.1.0]butanes A though singlet cyclobutane-l,3-diyls B
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Fluxional Molecules
Polytopal rearrangements
• Berry pseudorotation
• Turnstile rotation
Fluxional Molecules
MeaN-P;
Me£i—P,
r.TT,,r,,m.p-nT)rrnrmf1
XJLX
I .... I , . i ,,,,,, ,
juuuul _jLJJUjL
Fluxional Molecules
Non-mutual / Nondegenerate Exchange
Two or more distinquishable rotamers (at a low temperature) Isomerization
Stereochemical^ non-rigid molecules ^^^^^^^^^m
o H^^V^I
unequal populations (p) equilibrium constant K
Stereochemically Non-rigid		
Molecules		
		
		
	\ /	
	OC      CO \s<V	
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Study of Dynamic Processes in Solution by VT NMR
1. Indications of dynamic processes in solution:
• broad lines
• number of lines lower than expected
• dilution changes the spectrum
(indication of intermolecular processes) B+ C
• the change of the temperature changes the spectrum
• the addition of the molecules that participate in intermolecular processes changes the spectrum
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namic Processes bv VT NMR
2. Recording of the spectra at different temperatures, if accesible in slow exchange, at coalescence and in fast exchange. Slow exchange limit (static conditions) is particulary important.
3. From slow exchange limit the species participating in dynamic processes are identified. Simulate the static spectrum. The chemical shifts, coupling constants, natural line-width and concentration is needed for the spectrum of each species.
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namic Processes bv VT NMR
4. The possible dynamic processes are selected. Help with dilution of solution, addition of substance that could participate in processes, the free ligand or isotopically-labeled free ligand for example (intra- or intermolecular process).
5. Construct the exchange scheme = How the nuclei exchange their sites in the dynamic processes.
6. Simulate the spectra at the temperatures above the slow exchange limit by increasing the rate of the processes and/or changing the equilibrium concentrations. Compare the simulated and experimental spectra.
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namic Processes bv VT NMR
7. The matching of experimental and simulated spectra means that the dynamic process in possible. Remember to consider other possibilities. You can never prove a mechanism, only disprove one. For example, perhaps there are two processes being observed, not just one.
8. The reaction rates from simulation of spectra are pseudo first order rate constants (reciprocal life-times of the nucleus at the site). The rates of the real dynamic processes are related to these first order rate constants.
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namic Processes bv VT NMR
9. The Eyring plot of ln(k/T) versus i/Tresults in activation enthalpy and activation entropy.
10. The van't Hoff plot of ln(K) versus J/Tresults in reaction enthalpy and reaction entropy.
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(r)5-Cp)2Fe2(CO)4
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XH NMR of (Y15-Cp)2Fe2(CO)4
NMR of (y)5-Cp)2Fe2(CO)
•62.3
S0.2     - IS.I     -B2,3 -50.2
S (ppm) VS. CSZ
XH VT-NM R Spectrum of Cyclohexane-ď^
13C NMR Ci>-l54-dimethylcyclohexane
Fast exchange
Slow exchange
30 °C
2CH3
Ring Whizzing
H
H-NMR
34B Kl
317KI
275K
256K
Z38KI
21SK
Heissenberg Uncertainity Principle
AE At > h/2n
h = 6.626 10"34 J s
The broadening results from the finite lifetime of the spin states involved in the transition.
Energy levels are 'blurred' more for a shorter-lived state (because of the uncertainty relation).
As k increases at higher temperatures, the states involved in each transition have a shorter life-time and hence the uncertainty in each energy involved increases
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Heissenberg Uncertainity Principle
AE At > h/27i        h = 6.626 10"34 J s At = xA lifetime in site A [s]    At = TB lifetime in site B [s] 1/t = l/xA + l/xB ta = 1/kfo^   xB = 1/k^
AE = h/(2nxj
Line Shape Analysis
Two-State First Order Exchange Line shape
g(v) = intensity at the frequency V Variables vA, vB, T - changed to fit experimental spectrum
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Slow Exchange
Slow Exchange
(less than ~20% overlap)
Av0 = vA - vB
the separation between two peaks with no exchange
CO = line width at the half
of the peak maxima at the given
temperature
C0o = line width at the half
of the peak maxima
at the slowest exchange (no exchange)
Intermediate Exchange
Intermediate Exchange
(more than ~20% overlap)
AvQ = the highest separation between two peaks at the slowest exchange
Av = separation between two peaks at a given temperature
2
AvQ depends on B(
Coalescence
Coalescence kc = n AvG / 21/2 Coalescence temperature Tc
AvQ = the highest separation between two peaks at the slowest exchange
T > Tc, fast exchange
T < Tc, slow exchange
Coalescence
Gutowsky—Holm equation
k = k * kB T / h * exp (-AG*/RT)
k = k* kBT/h* exp( AS*/R) * exp(-AH*/RT)
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Fast Exchange
Fast Exchange
(10 - 15 K above the coalescence point)
k = 7T Avo2 /2(G) - co0)
Avo = the highest separation between two peaks at the slowest exchange
CO = line width at the half of the peak maxkna at the given temperature
CD0 = line width at the half of the peak maxima at the slowest exchange (no exchange)
A single resonance is observed, whose chemical shift is the weight average of the chemical shifts of the two individual states
lange
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Fast Exchange
Fast Exchange
A single CH3 resonance is observed, whose chemical shift is the weight average of the chemical shifts of the two individual states
Equilibria
Fast processes (ms) = averaged singlet spectrum on NMR timescale (s)
• equilibria are temperature dependent
• exchanging species have different chemical shifts
• difference in enthalpy similar to the entropy difference times an accessible temperature
• the averaged chemical shift vary with temperature
• the chemical shift measured at many temperatures
• the values of the chemical shifts of each state
• enthalpy difference and entropy difference can be determined by a fitting function
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Equilibria
S = (l-p)SA + pSi
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Acid-Base Equilibria
Exchange in Coupled Systems
Solvents for DNMR at Low Temperatures
Solvent	B.p. °C (1 atm)	M.p. °C (1 atm)
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		-168
		
		
Solvents for DNMR at High Temperatures
Transition State Parameters
Medium fast (s) exchanges = line broadening.
At the fast regime - a broadened singlet spectrum Slow exchange - the spectrum splits into two narrowing to two sharp spectra at slow exchange
Varying the temperature changes the exchange rate the determination of thermodynamic constants of the transition state
the transition state paramters for the exchange between two states at the same energy.
57
Transition State Parameters
k = nÖv/2(w-w0) k =KBTQxp{-AGxIRT)l2h AGX = AHX - TAS1
k = rate constant, Sv = peak separation, w = observed line width, wa is natural line width, kB = Boltzmann constant (1.38062xl0~23 J/molK), R= gas constant (8.3143 J/Kmol), T = temperature, AG* = free energy, AS* = entropy, AH* = enthalphy, h = Plank's constant (6.62620xl034 Js).