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

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

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

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

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

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

Cycloaddition

Photochemical reactivity Under thermal conditions Under photo-excitation

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

Reactivity GTP 8-O-GTP

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

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

Dynamical changes

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

Active site effect

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

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

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

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.

Dynamic reaction models mov/react/triton.mpeg

ΔG‡-1 ΔG‡ DG

Derived properties

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

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

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

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

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 ( -1060 · DGreaction) in a. u. at 300K: Keq ≈ e ( -1060 · DEreaction) in Kcal/mol at 300K: Keq ≈ e(-1.67739 · DEreaction)

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 ( -1060 DE‡)

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

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