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On the subsystem formulation of linear-response time-dependent DFT.

Michele Pavanello¹

¹Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA. m.pavanello@rutgers.edu

The Journal of Chemical Physics

|June 8, 2013

Summary

This study presents a new derivation of subsystem time-dependent density functional theory (TD-DFT), revealing complex relationships between subsystem and supersystem electronic spectra. Kohn-Sham response is found to be non-additive, an artifact of density partitioning.

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Area of Science:

Computational Chemistry
Quantum Chemistry
Theoretical Chemistry

Background:

Linear-response subsystem time-dependent density functional theory (TD-DFT) is a method for calculating electronic properties of large systems by dividing them into smaller subsystems.
Existing formalisms for subsystem TD-DFT have limitations in fully characterizing the response properties and their relationship to the supersystem.
Understanding the additivity and partitioning effects in subsystem DFT is crucial for accurate electronic structure calculations.

Purpose of the Study:

To provide a thorough and novel derivation of linear-response subsystem TD-DFT.
To derive and analyze Dyson-type equations for subsystem TD-DFT, revealing new insights into response functions.
To compare the properties of subsystem TD-DFT response functions with those of the supersystem TD-DFT.

Main Methods:

Developed two equivalent derivations for self-consistent subsystem TD-DFT equations.
Derived Dyson-type equations involving coupled, uncoupled, and Kohn-Sham subsystem response functions.
Analyzed the pole structure of subsystem response functions and compared them with supersystem response functions.

Main Results:

The new derivations yield self-consistent subsystem TD-DFT equations, with one matching Neugebauer's formalism and the other introducing Dyson-type equations.
Subsystem response functions contain information about the electronic spectrum of the entire supersystem.
Correlated response is subsystem additive, but Kohn-Sham response is not, with non-additivity attributed to subjective density partitioning.

Conclusions:

The derived Dyson-type equations offer a new perspective on subsystem TD-DFT.
The analysis highlights previously unrecognized complexities and qualities of subsystem TD-DFT compared to supersystem TD-DFT.
The non-additivity of Kohn-Sham response is an artifact of density partitioning, suggesting potential improvements in partitioning schemes.