1. Chemical Reactions José R. Valverde CNB/CSIC jrvalverde@cnb.csic.es
CC-BY-NC-SA

2. Index Goals FMO theory Transition State calculations
Reaction Coordinate calculations
Derived properties
Limits

3. Goal Predict compound reactivity Predict reaction mechanism
Compute reaction path and energies
Calculate derived properties for experimental validation
Compare properties between mutants/ligands

4. Some terms e- donor: nucleophile, base, reductor
must be an occupied orbital
e- acceptor: electrophile, acid, oxidizer
must be an unoccupied orbital

5. Frontier Molecular Orbitals
Reactions wih small energy barriers are favored
The smaller the difference in energy among orbitals, the more favorable the reaction
Orbitals normally have increasing energy as they distance from the nucleus
The HOMO has the highest energy among occupied orbitals
The LUMO has the lowest energy among unoccupied orbitals

6. Simple FMO Theory HOMO + LUMO -> bonding MO
HOMO + HOMO -> antibonding MO
LUMO + LUMO -> null (no e-)
SOMO + SOMO -> bonding MO

7. Cycloaddition

8. Photochemical reactivity
Under thermal conditions
Under photo-excitation

9. 8-oxo-GTP GTP HOMO LUMO Computed with ErgoSCF at the
6-31G** level from PDBechem entries 8GT and GTP
LUMO

10. Reactivity
GTP
8-O-GTP

11. Dynamic changes
mov/QM/gtp-bnd-lumo.avi

12. Dynamic changes
mov/QM/8ogtp-bound-lumo-wire.avi

13. Dynamical changes

14. SN2 reaction A nucleophile (e- donor) attacks an electrophile
breaking a bond and releases
a leaving (L) group.

15. Active site effect

16. Accurate modeling
Explore conformational space to find lowest energy path
Beware of tunneling effects
Transition State Search
Reaction Coordinate Path
Quantum Dynamics

17. Transition state Can be computed from reactants and products
A good intuition of the reaction path helps
From TS, activation energy
can be computed.

18. Saddle calculations Optimize reactant Optimize product
Optimize product using reactant as reference
Optimize reactant using closer product as reference
Using the intermediate geometries, run a SADDLE calculation
Use the result for a Transtion State calculation

19. Reaction coordinate The reaction is modelled from reactants
The two atoms reacting and their relative path must be specified
Some methods allow for specification of the atoms only and explore the space.

20. Dynamic reaction models
mov/react/triton.mpeg

21. ΔG‡-1
ΔG‡ DG

22. Derived properties

23. Balanced reactions reactants <--> products
DEreaction = SEproducts - SEreactants
DE < 0 => exothermic, favorable
DE > 0 => endothermic, unfavorable

24. Isomer stability isomer1 <--> isomer2
DEisomer = Eisomer2 - Eisomer1
DE < 0 => isomer2 is more stable

25. Activation energy
DE‡ = ETS - Ereactants
TS = Transition State

26. Free Energy DGrxn = DHrxn - T DSrxn
DHrxn = enthalpy of rxn ≈ DErxn = SDEprod - SDEreac
T = Temperature
DSrxn = entropy of rxn = SDSprod - SDSreac
In most reactions DS can be neglected
DGrxn ≈ DHrxn ≈ DErxn

27. Equilibrium constant
Keq = e ( - DG / RT ) DGreaction = - R · T · ln Keq
Keq = equilibrium constant
DGreaction = Free energy of the reaction
R = Gas constant
T = Temperature in ºK
Keq = e ( · DGreaction)
in a. u. at 300K: Keq ≈ e ( · DEreaction)
in Kcal/mol at 300K: Keq ≈ e( · DEreaction)

28. Reaction rate Krxn is related to DG. If entropy is neglected
Krxn = (Keq T h) · e ( -DE‡ / R T)
Keq = Boltzmann's constant
h = Planck's constant
DE‡ = Activation energy
In a.u. at 300K: Krxn = 6.2 · 1012 · e ( DE‡)

29. Half life (t½)
Amount of time taken for the reactant concentration to drop to 1/2 the original value.
For a first-order rate reaction
rate = - Krxn [reactant]
t½ = ln 2 / Krxn = 0.69 / Krxn

30. Thanks To all of you For coming... and not falling asleep
To the organizers
For this wonderful opportunity
To CNB/CSIC, EU-COST, CYTED
For funding