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
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Spectroscopic Observation of Dynamical Processes
A unique tool for investigating processes without perturbing the system
NMR spectroscopy UV-VIS spectroscopy IR spectroscopy (EPR spectroscopy)
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I
Spectroscopic Observation of Dynamical Processes
Irreversible reactions:
For slow reactions (rate constants for the reactions are lfr6 to lfr3 s'1 typically): 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
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Timescale of Chemical Processes
Spectroscopy Typical
frequenc differen
= 2.22
ocesses occurring o
is timescale
8
termolecular
ocesse
Intramol
uclei or electron ovement)
111
On
tramolecular electro
vement
Chemical Exchange
NMR time scale:  ms to jlxs
Reversible processes
Activation energies 20 — 100 kj mol-1
Stable isomers at room temperature AG* >100kjmol"1
Methods:
• Band shape analysis 20 - 80 kj mol"1
• Polarization transfer 80 - 100 kT mol-1
Temperatures -150 / +150 °C
T = 273 K k - 500 s"J
Reaction Coordinate
A_G° = -RT InK
ArG° = ArH° - T ArS'
AG * = - RT In K*
AG * = AH* - T AS*
Intramolecular Mobility
N
N
"N" N'
,CH3
N
CH3
CH,
N N
CH3
AG* = AH*-T AS*
Possible separation at r.t
Direct equilibration
160 120
Flash photolysis
MW
NMR
ESR
80
40
AG* kJ mol
Bond Energies
covalent bond 100-600 kJ/mol
coordination bond molecular 40-120 kJ/mol interactions
2-50 kJ/mol
hydrogen bond
Reaction Rate
Arrhenius equation
Theory of Activated Complex
k3
A (g) + B (g) S+ [ActC]* -> P(g) + Q(g)
Equlibrium constant of activated complex K* = [ActC]* / [A] [B]
Rate = fc, [ActC]* = k, K* [A] [B]
k3 = tf =tkBT/h
t = transmission factor (=1) f = frequency of ActC decomp.
Rate = (t kRT / h) Kl [A] [B]
k = (t kRT / h) K*
AG * = - RT In K*
AG * = AH* - T AS*
Eyring Equation
Rate = (t kBT / h) K* [A] [B] k = (t kRT / h) K*
I
use:    AG * = - RT In K* AG*= AH*-T AS*
t = transmission factor = 1
h
1 tkBT
In—5—
tkBT
exp
V
RT
J
tkBT
exp
V
-AH RT
exp
AS
V
R
J
= ln
h tk
AH* AS* --h
RT
B
h
R
AH* AS* -+
RT
Activation Parameters
R
+ 23.76
Thermodynamics
Energy change [kJ/mol]
AS approx. +200 J/mol K
o—o = o o
coordination bond molecular bond hydrogen bond
forAH = 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, T = 300K
K = 6x106,     T = 200 K
Kinetics
coordination, molecular or hydrogen bonds edducts        m products
for AG* = 60 kJ/mol
AG* = RT[23.76 -ln(k/T)]
k = 600 s-1 T = 300 K k = 0.0009 s-1 T = 200K
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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
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
Mutual/Degenerate Exchange
Only one distinauishable molecule Cat a low temperature
Fluxional molecules, topomerization
AG°= 0
Fluxional Molecules
Bridging — terminal exchange
Fluxional Molecules
Polytopal rearrangement
Berry pseudorotation
lurnstlle geometry
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Fluxional Molecules
Mfl&N—P
F
F
_~__
J
|-T..1ir.fFr.Tr|n-.iytT.. I " " T
L JL
JJ
J
l.n^.n^rfrnr, rr,,^-. q I""!'"'!----1 ■ ■ ■ 'I""" I" "1
JLAJUL JUu
r,..x,----T----|.~.|----l----i r ■ "i >■■■!■'■ ■!----i----I
_jLIUULJL. XJJJLJLjL
TTf    T, | .... f .... r ....... * * f i-, . , t., , .. ..   • j----f----r' - "i
Fluxional Molecules
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Non-mutual / Nondegenerate Exchange
Two or more distinquishable rotamers (at a low temperature) Isomerization
Stereochemical^ non-rigid molecules AG°^0
unequal populations (p) equilibrium constant K
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Stereochemically Non-rigid
Molecules
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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) ^^Hl 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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Dynamic Processes by 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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Dynamic Processes by 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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Dynamic Processes by 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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Dynamic Processes by VT NMR
9. The Eyring plot of ln(k/T) versus X/T results in activation enthalpy and activation entropy.
10. The van't Hoff plot of ln(K) versus 7/7^results in reaction enthalpy and reaction entropy.
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aH NMR of (v]5-Cp)2Fe2(CO)4		
		■dM"              /\                         .0160 sec j\
	°\ ..-i ^ °\ ...i r	jNs^ —^ ^— 1
Cis — Trans isomer exchange		
C NMR of (v15-Cp)2Fe2(CO)4
-Ä9-
+ 55"
65'
+ 44'
ahIs,-^-\*
SE.3       -50.2     - 1BJ      -Ů2.3     -50.2 -1SJ
S (ppm} vs. CSZ
*H VT-NMR Spectrum of Cyclohexane- du
XH VT-NMR Spectrum of Cyclohexane-i/^
BC NMR (ľ/5-l,4-dimethylcyclohexane
*      3 ř
30 °C
-60 "C
4 Ctttfpň CHjfijŕj
Two-State First Order Exchange
TA lifetime in site A [s]
TB lifetime in site B [s]
orw
1/t = l/xA+ 1/tb     single lifetime
i
forw
rev
I T				
				
Heissenberg Uncertainity Principle
AE At > h/2
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 A-increases at higher temperatures, the states involved in each transition have a shorter life-time and hence the uncertainty in each energy involved increases
l
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Heissenberg Uncertainity Principle
AE At > h/2
h = 6.626 10-34 J s
At = xA lifetime in site A [s]    At = xB lifetime in site B [
1/x = l/xA + 1/x,
xA = l/kforw   xB = 1/k,
AE = 11/(271^
AE = hAVi,
h/(27t x) = h Av,
Av1/2 =(7tx)-
AVi/ = linewidth
Line Shape Analysis
Two-State First Order Exchange
B
krev
Variables VA, VB,'		I - changed to	fit experimental spectrum
		const(vA -vB) t	
		-vB)-v	2 + 47t2t\va-v)\vb-v)2
Av0 = vA - vB the separation between two peaks with no exchange
k = 71 (CO - C0o)
G) = line width at the half of the peak maxima at the given temperature
(D0 = 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
I
AvQ depends on B(
Coalescence kc = 7iAv0/21/2
Coalescence temperature T
AvQ = the highest se two peaks at the sky
T > Tc, fast exchange
T < Tc, slow exchange
Fast Exchange
Fast Exchange
(10 - 15 K above the coalescence point)
Avo = the highest separation between two peaks at the slowest exchange
CD = line width at the half of the peak maxima at the given temperature
G)0 = line width at the half of the peak maxima' at the slowest exchange (no exchange)
Fast Exchange
Fast Exchange
(10 - 15 K above the coalescence point)
Av.
A single resonance is observed, whose chemical shift is the weight average of the chemical shifts of the two individual states
/l+/2=l
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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
Sobs = PlSA + PlSl Pl+P2=1
Pava + Vi
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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S = {l-p)ôA+pSi
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Exchange in Coupled Systems
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Solvents for DNMR at Low Temperatures
Solvent
B.p. °C (1 atm)
M.p. °C (1 atm)
iL«]
Vinyl ch
Solvents for DNMR
at High Temperatures
Solvent		B.p. °C (1 atm)
CI2CDCDCI2		EE??
CHBr3		
		
o-Dichlorobenzene		
Benzonitrile		
Hexachloro-1,4-butadier		
Br2CDCDBr2		
Diphenyl ether		
		
Transition State Parameters
I
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.
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Transition State Parameters
k =KBTQxp{-AGxIRT)l2h AGX = AH1 - TAS1
— rate constant, Sv — peak separation, w — pbserved line width, w0 is natural line width, kB Boltzmann constant (1.38062xl0~23 J/molK), =   gas   constant   (8.3143   J/Kmol),   T = emperature, AG* = free energy, AS* — entropy, ->  enthalphy,   h   —   Plank's constant (6.62620xl(T34 Js).