scholarly journals Toward a Resolution of the Static Correlation Problem in Density Functional Theory from Semidefinite Programming

2020 ◽  
pp. 385-391
Author(s):  
Daniel Gibney ◽  
Jan-Niklas Boyn ◽  
David A. Mazziotti
Keyword(s):  
Density Functional Theory ◽  
Semidefinite Programming ◽  
Density Functional ◽  
Functional Theory ◽  
Correlation Problem ◽  
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 Range-Separation and the Multiple Radii Functional Approximation Inspired by the Strongly Interacting Limit of Density Functional Theory

2019 ◽  
Author(s):  
Stefan Vuckovic ◽  
Tim Gould
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Approximate Theory ◽  
Exact Results ◽  
Strong Correlations ◽  
Functional Theory ◽  
One Dimensional ◽  
Strongly Interacting ◽  
Correlation Problem ◽  
Exactly Solvable

The strongly-interacting limit of density functional theory has attracted considerable attention recently due to its ability to deal with the difficult strong correlation problem. Recent work [JPCL 8, 2799-2805 (2017)] introduced the "multiple radii functional" (MRF) approximation, inspired by this limit, which is designed to work well for strong correlations between dissociated fragments. Here, we analyse the MRF in exactly solvable one-dimensional molecules, to uncover how it matches, and deviates from, exact results; and use range-separation of the Coulomb potential in both exact and approximate theory to explore how this varies in space. Our work opens a path to new approximations incorporating the MRF, amongst other ingredients.<br><br>

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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