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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

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Linear-scaling quantum mechanical methods for excited states.

ChiYung Yam¹, Qing Zhang, Fan Wang

¹Department of Chemistry, The University of Hong Kong, Hong Kong.

Chemical Society Reviews

|March 16, 2012

Summary

Linear-scaling (O(N)) quantum mechanical methods enable excited-state calculations for large systems. Time-domain methods are more mature and stable than frequency-domain approaches for complex molecular dynamics.

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Area of Science:

Quantum mechanics
Computational chemistry
Theoretical chemistry

Background:

Traditional quantum mechanical methods struggle with scaling for large systems.
Excited-state calculations are crucial for understanding molecular properties and dynamics.
Linear-scaling (O(N)) methods offer a solution for computationally demanding systems.

Purpose of the Study:

To review recent advancements in linear-scaling (O(N)) quantum mechanical methods for excited states.
To categorize and compare time-domain and frequency-domain O(N) approaches.
To highlight the applicability and limitations of these methods for various response properties.

Main Methods:

Focus on locality-based O(N) methods for excited states.
Categorization into time-domain (real-time dynamics) and frequency-domain (electronic response) methods.
Discussion of the localized density matrix (LDM) method and time-dependent Kohn-Sham (TDKS) with non-orthogonal localized molecular orbitals (NOLMOs).

Main Results:

The localized density matrix (LDM) method is a mature O(N) approach implemented in both domains.
O(N) frequency-domain methods face convergence issues for resonant responses in most systems.
For linear response, LDM with Chebyshev expansion is efficient; for off-resonant nonlinear response, iterative frequency-domain methods are practical.
Time-domain methods are versatile for nonlinear responses but computationally expensive; O(N) semi-empirical methods offer a practical alternative.

Conclusions:

O(N) time-domain methods for excited states are more mature, stable, and widely applied than frequency-domain counterparts.
Time-domain methods are essential for investigating the dynamics of complex molecular systems.
The choice between time- and frequency-domain methods depends on the specific response property and system characteristics.