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Following the Dynamics of Structural Variants in Experimentally Evolved Populations

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Density-functional expansion methods: Grand challenges.

Timothy J Giese¹, Darrin M York¹

¹Department of Chemistry and Chemical Biology and BioMaPS Institute for Quantitative Biology, Rutgers University, Piscataway, NJ 08854-8087.

Theoretical Chemistry Accounts

|June 14, 2016

Summary

This summary is machine-generated.

Semiempirical density functional expansion (VE) methods accurately model Kohn-Sham methods but introduce errors due to approximations in basis sets and core-Hamiltonian treatments. New models and insights aim to improve these computational chemistry techniques.

Keywords:

Tight-binding models density functional theory electronic structure

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Area of Science:

Computational Chemistry
Quantum Chemistry
Materials Science

Background:

Semiempirical methods offer a computationally efficient alternative to ab initio calculations in quantum chemistry.
Density functional theory (DFT) and Kohn-Sham (KS) methods are widely used for electronic structure calculations.
Semiempirical density functional expansion (VE) methods aim to bridge the gap between accuracy and computational cost.

Purpose of the Study:

To identify and analyze the sources of errors in semiempirical density functional expansion (VE) methods.
To compare the performance of VE methods with their standard Kohn-Sham (KS) counterparts.
To propose new theoretical models and approximations for improving VE methods.

Main Methods:

Analysis of approximations in VE methods: limited atomic orbital basis sets, Slater monopole auxiliary basis for response density, and core-Hamiltonian matrix element treatments.
Introduction of a new model supplementing the second-order density-functional tight-binding (DFTB) model with charge-dependent chemical potential equalization.
Generalization of the auxiliary basis description for atomic orbital response density.
Decomposition of the first-order potential into atomic components and many-body corrections.

Main Results:

VE methods can closely reproduce standard KS methods when approximations are minimized.
Significant errors arise from approximations in basis sets, auxiliary basis descriptions, and core-Hamiltonian treatments.
New insights into the first-order potential decomposition motivate novel approximate treatments for the core-Hamiltonian.

Conclusions:

Understanding the specific approximations is crucial for mitigating errors in VE methods.
The developed models and analytical approaches provide a foundation for more accurate and efficient semiempirical calculations.
Further research into approximate core-Hamiltonian treatments is warranted to enhance VE method performance.