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Density Functional Theory to modelling electron-transfer rea

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Felix Hernandez

on 7 May 2014

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Transcript of Density Functional Theory to modelling electron-transfer rea

Density Functional Theory to modeling electron-transfer reactions
The electron-transfer reaction
A theory to describe the system
General description
Two states
Donor (D)
Acceptor (A)
What is an electron-transfer reaction?
“The transfer of an electron from one molecular entity to another, or between two localized sites in the same molecular entity.” (PAC, 1994, 66, 1077. Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994))

Examples of ET reactions:
Anaerobic respiration
The electron is transfer from donor to acceptor
The charge is externally introduced/extracted:
The charge is separated:

The electronic coupling between D and A
The quantum-mechanical approach
The Marcus Theory
Based on the ideas:
Fast movement of the electrons
The Frank-Condom principle applied to electron-transfer reactions
Conservation of the total energy of the system
Dielectric continuum theory to solvent molecules

Defined by:
Depending on its value
Adiabatic electron-transfer reactions
It causes a split in the intersection point
Diabatic electron-transfer reactions
Relatively strong electron coupling
Reaction occurs as a "jump"
Small probability per passage through the intersection region
Very weak electronic coupling
Modern approaches to the problem
What is an electron reaction?
Long-range ET reactions
Tunneling is the main mechanism
Well described by diabatic states
The classical expression does not account for tunneling effects
New expression is needed
High temperature limit
Equal to the classical equation
It account with tunnel effects

Reorganization energy
Driving Force
Electronic coupling
Constrained DFT
Frozen Density Embedded
Density Functional Theory
Hohenberg-Kohn theorems
The density is uniquely determined by an external potential
The ground state energy is a functional of the density
The Kohn-Sham formalism
Density of a non-interacting system
The Kohn-Sham energy functional
Approximations to
ET reaction rates calculated with TD-DFT
Main issues:
Diabatic states obtained from adiabatic states (ground and CT states need to be computed)
Impossible to generate charge-localized states (SIE)
Too low charge-transfer excitation energies
Wrong asymptotic behavior at long distances
Poor description of ET reactions
We need a way to generate charge-localized states
Impose a constraint into the system
Generate charge-localized states
Obtain the information needed to calculate the ET reaction rate
Defining a constraint
weight function defining the property
constrained observable
The system is optimized under the constraint
Looking for stationary points yield
Initial guess ρ
Calculate orbitals with the KS equation
Recalculate the orbitals with the above equation
outer loop
inner loop
How to define the fragments
Atomic populations schemes are used to define the wight element
(Mulliken, Löwdin, Becke or Hirshfeld)
Charge localized states obtained from two constrained DFT calculations
First charge-localized state
N = -1
N = 1

Subsystem density formulation
Generate charge-localized states
Obtain diabatic states

Subsystem density formulation
Total density of the system
A functional for the energy
Nonadditive kinetic energy term
In general, a non linear function satisfies :
The same is applicable for a nonlinear functional
The nonadditive term represents
In addition to
we need to approximate
Similar to KS one-electron equations
The effective potential is defined as
It is solved self-consistently
obtained from a KS calculation for the isolated subsystem
freeze-and-than cycle
How to define define the fragments
Subsystem B
Subsystem A
Subsystem B defined with an extra charge
It enter in the optimization process with the charge already constrained within this fragment
We obtain the density of one charge-localized state
The same procedure to generate the charge-localized state of products
DFT calculations of the whole system
DFT calculations on smaller subsystems
Two ground-state DFT calculations
Four ground-state DFT calculations (minimum)
Large systems are computationally demanding
Large system are calculated adding more subsystems
Charge-Transfer excited states avoided
Activated complex
The system remains in the GS
Introduced through a Lagrangian into the inner loop
Defined as the difference in charge
Constraint property
from KSCED eqn.
Second charge-localized state
The total energy is obtained:
Freezing subsystem B
Freezing subsystem A
Which terms can we extract?
Two charge-localized states:
They are difference because states A and D are not orthogonal
The electronic coupling is obtained after diagonalizing the Hamiltonian matrix
Which terms do we obtain?
The two charge-localized states are obtained
The CT excitation energy
Electronic coupling
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