1 Advanced Theories of Chemical Bonding Chapter 10 Atomic Orbitals Molecules.
Introduction to Theories of Chemical...
Transcript of Introduction to Theories of Chemical...
Introduction to Theories ofChemical Reactions
Graduate Course SeminarBeate Flemmig
FHI
I. Overview
What kind of reactions?
• gas phase / surface• unimolecular / bimolecular• thermal / photochemical
What kind of information?
• structure of reactants, products• ΔEreact• mechanism• TS, Ea• k• τ, lifetime of intermediates
What kind of theoretical approach?
• MO and VB theoryalmost without calculation, based on symmetryarguments
• Quantum ChemistryBorn-Oppenheimer approximationsolution of electronic Schrödinger equationoptimization of stationary points of PESfollow IRCTD data → TS theory
• Molecular Dynamicssemiempirical potentialor calculation of forces ‘on the fly’ (CPMD)T ≥ 0
• beyond BO (wave-packet dynamics)more than one PES (photochemistry!)solution of nuclear SEreal-time evolution of a chemical reactionrelated to “pump-probe“ spectroscopy or ”femtosecondchemistry”
• statistical mechanicsmany particles
An attempt to summarize the approaches …
R. Daudel, Quantum Chemistry, John Wiley, p. 299
a: number of particles
x: electronic coordinates
X: nuclear coordinates
t: time
II.ExampleReaction:Chelate RingInversion
Organometallics, 22 (2003) 1196.
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k(TC ) =RTCNAh
e−ΔEa
RTC
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k(TC ) =π
2Δν
experimentally ΔEa 62 kJ/mol from 1H NMR
H. Köpf, Angew. Chem. 83, 146-147, (1971)
M. Hesse, H. Meier, B. ZeehSpektroskopische Methoden in derorganischen Chemie Thieme Verlag 1991
approximate formulaΔν between signalsof H at the twoC5H5-rings
coalescence temp.TC (~ 20 ºC)
Stabilizing and destabilizing effects of folding
Lewis structure
III. Application of MO TheoryRing opening and closing of ozone - A forbidden reaction
molecular plane σ preserved in the reactionlevels of MOs with different symmetry w. r. t. σ are crossing
computed* kinetic persistence of the cyclic isomer* K. Ruedenberg et al. J. Chem. Phys. (1991) 94 8054.
life time of the intermediate
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k = Ae−EaRT
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τ ~ 1k
Arrheniusequation
half-life time
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d xd t
= k c0−x[ ]
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ln c0c0−x
= kt
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x := 12c0
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t :=τ
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τ = ln2k−1
unimolecular reaction
first-order rate law
Fill in numbersassume preexponential factor of 1015s-1 (unimolecular reaction)
calculated barrier 23 kcal/mol = 95.7 kJ/mol (the lower one)
room temperature 25ºC
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k = Ae−EaRT
k =1015s−1e−95.7kJmol-1
8.31JK−1mol−1298K
k =0.64 ⋅10−2s-1
τ = ln2k−1
τ = 44 s
Use cyclic ozone as a ligand
6 π electron donor
applied an ‘18-electron strategy’
Some Predicted Complexes
Transition Metal Complexes of Cyclic and Open Ozone and Thiozone Flemmig, B.;Wolczanski, P. T.; Hoffmann, R. J. Am. Chem. Soc. 2005 ASAP Article
Woodward - Hoffmann Rules
to explain stereoselectivity of cycloadditions
different symmetry elements remain,depending on the mechanism
correlation diagram: level-crossing for disrotatory path
see also: R. Hoffmann, Angew. Chem. Int. Ed. (2004) 43, 6586 - 6590
coefficients ofHückel
solutions(π systems)
correspond toparticle-in-a-box solutions
VB-Theory
S. Shaik, A. Shurki, Angew. Chem.Int. Ed. (1999) 38, 586 - 625.
IV. Application of QuantumChemistry
use Born-Oppenheimer approximation
and solve the electronic Schrödinger equation (for fixed R)
ideally: determine electronic properties as functions ofnuclear coordinates - i. e. determine the PES
Potential Energy Surface, PES:
• governs nuclear motion, forces on the nuclei Fx = -∂E/∂x
• stationary points correspond to (meta)stable species (local orglobal minima) and to transition states (saddle points)
• shape of PES around stationary points determinesvibrational spectra
• electronic transitions correspond to transitions from onePES to another
• minimum energy path corresponds to reaction coordinate
in reality: Calculated PES only available for very small systems,for example H+H2 in colinear arrangement
without Coulomb interactions with Coulomb interactions
H. Eyring, M. Polanyi, 1931 M. Karplus et al. 1968
in practice: stationary points of PES, their characterization(frequency calculations), and maybe the reaction path (IRCcalculation)
Transition State Theory
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k =kbTh
QTS
QR e−Ea
k bTEyring equationH. Eyring, J. Chem. Phys. (1935) 3, 107
partition function
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Q = g jlevels∑ e
−ε j
k bT
εvib = n +12
hν
Example: Study of a Radical ClockRearrangement on a Surface
FTIR: ring modes at1393 cm-1and 1434 cm-1 vanish andC=C stretch mode emerges at 1645 cm-1
C. M. Friend, I. Kretzschmar, JACS (2000) 122 12395.
Cyclopropylmethoxide and 3-butenyloxide on Mo(110)
Flemmig, B.; Kretzschmar, I.; Friend, C. M.; Hoffmann, R. J. Phys. Chem. A. 2004; 108(15) 2972-2981
ΔEtotal = 31 kJ/mol
Alternative mechanisms already for the isolated molecule
Which is the rate-determining step ?
… the one with the highest activation energy (not the onewith the highest barrier)
see also: H. Eyring et al. The Theory of Rate Processes, McGraw Hill, New York 1941.
V. Molecular Dynamics
classical equations of motion€
H = TK +U
TK =12
PI2
MI∑
nuclei have kinetic energy TK > 0
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U :Te (r) + VeK (r,R) + Vee (r) + VKK(R)PI : classical momentum
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RI•
=∂H∂PI
PI•
= −∂H∂RI
solutions RI(t) and PI(t) are the trajectories of the nuclei
VI. Wave-Packet Dynamicstreat also the nuclei quantum-mechanically
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HΦ(R,t) = ih ∂∂tΦ(R,t)
H = TK +U+ [Hextern ]
TK =h2
2∇2
MI∑
simulations only for intervals of a few picoseconds
very fast reactions: e.g. laser-induced isomerizations
R
R
ϕ
References/Acknowledgement
• C. Engler (Uni Leipzig) Überblick über dieNäherungshierarchie und Lösungsansätze in derQuantentheorie, Graduate Course
• H.-J. Werner (Uni Stuttgart) Computational Chemistry inCatalysis, Graduate Course
• R. Hoffmann (Cornell) Bonding in Molecules, CHEM798
• W. J. Moore, D. O. Hummel, Physikalische Chemie, deGruyter Berlin 1986.