scholarly journals Dispersion, static correlation, and delocalisation errors in density functional theory: An electrostatic theorem perspective

2011 ◽  
Vol 135 (16) ◽  
pp. 164110 ◽  
Author(s):  
Austin D. Dwyer ◽  
David J. Tozer
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Functional Theory ◽  
Static Correlation

scholarly journals Hole-Hole Tamm-Dancoff-Approximated Density Functional Theory: A Highly Efficient Electronic Structure Method Incorporating Dynamic and Static Correlation

2020 ◽  
Author(s):  
Christoph Bannwarth ◽  
Jimmy K. Yu ◽  
Edward G. Hohenstein ◽  
Todd J. Martínez
Keyword(s):  
Density Functional Theory ◽  
Electronic Structure ◽  
Excited States ◽  
Density Functional ◽  
Random Phase ◽  
Computationally Efficient ◽  
Functional Theory ◽  
Complete Active Space ◽  
Dynamic Correlation ◽  
Static Correlation

<div> <div> <div> <p>The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field (CASSCF) methods neglect much of the dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we revisit hole-hole Tamm-Dancoff approximated (<i>hh</i>-TDA) density functional theory for this purpose. The <i>hh</i>-TDA method is the hole-hole counterpart to the more established particle-particle TDA (<i>pp</i>-TDA) method, both of which are derived from the particle-particle random phase approximation (<i>pp</i>-RPA). In <i>hh</i>-TDA, the <i>N</i>-electron electronic states are obtained through double annihilations starting from a doubly anionic (<i>N</i>+2 electron) reference state. In this way, <i>hh</i>-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. The treatment of dynamic correlation is introduced through the use of commonly-employed density functional approximations to the exchange-correlation potential. We show that hh-TDA is a promising candidate to efficiently treat the photochemistry of organic and biochemical systems that involve several low-lying excited states – particularly those with both low-lying pipi* and npi* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on <i>pp</i>-TDA and <i>pp</i>-RPA, we employ a functional-dependent choice for the response kernel in <i>pp</i>- and <i>hh</i>-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT.</p> </div> </div> </div>

scholarly journals Fractional spins and static correlation error in density functional theory

2008 ◽  
Vol 129 (12) ◽  
pp. 121104 ◽  
Author(s):  
Aron J. Cohen ◽  
Paula Mori-Sánchez ◽  
Weitao Yang
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Functional Theory ◽  
Static Correlation

A new exchange–correlation functional free of delocalization and static correlation errors

2014 ◽  
Vol 16 (31) ◽  
pp. 16373-16377 ◽  
Author(s):  
Yu Liu ◽  
Jianzhong Wu
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Correlation Energy ◽  
Density Approximation ◽  
Functional Theory ◽  
Weighted Density ◽  
Exchange Correlation ◽  
Static Correlation ◽  
Weighted Density Approximation

A combination of weighted density approximation and classical mapping leads to a new exchange–correlation energy free of delocalization and static correlation errors in Kohn–Sham density functional theory.

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