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Woodward-Hoffmann rules in density functional theory: initial hardness response.

Frank De Proft¹, Paul W Ayers, Stijn Fias

¹Eenheid Algemene Chemie, Vrije Universiteit Brussel (VUB), Faculteit Wetenschappen, Pleinlaan 2, 1050 Brussels, Belgium.

The Journal of Chemical Physics

|December 15, 2006

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Conceptual density functional theory (DFT) explains Woodward-Hoffmann rules using chemical hardness. This approach quantifies reactivity without wave function phase, offering new insights into pericyclic reactions.

Area of Science:

Organic Chemistry
Theoretical Chemistry
Quantum Chemistry

Background:

The Woodward-Hoffmann rules are fundamental for predicting pericyclic reaction outcomes.
These rules traditionally rely on the symmetry properties of molecular wave functions.
Conceptual density functional theory (DFT) offers a wave function-independent framework for chemical principles.

Purpose of the Study:

To reformulate the Woodward-Hoffmann rules using the language of conceptual DFT.
To investigate the utility of chemical hardness in explaining pericyclic reaction behavior.
To demonstrate that DFT concepts can explain phenomena traditionally requiring wave function phase analysis.

Main Methods:

Studied the initial chemical hardness response along model reaction profiles.

Related Experiment Videos

Examined two prototypical pericyclic reactions: Diels-Alder cycloaddition and ethylene dimerization.

Analyzed both singlet ground state and triplet excited state reaction pathways.

Main Results:

For thermally allowed/photochemically forbidden reactions, initial hardness response is positive in the singlet state and negative in the triplet state.
For photochemically allowed/thermally forbidden reactions, this hardness response behavior is reversed between singlet and triplet states.
The observed hardness responses correlate with the thermal and photochemical allowedness of the reactions.

Conclusions:

Chemical hardness, a DFT concept, effectively explains the Woodward-Hoffmann rules for pericyclic reactions.
This work establishes a quantitative, wave function-free approach to understanding pericyclic reaction mechanisms.
DFT-based chemical concepts provide valuable alternatives for explaining complex chemical reactivity.