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1. Density Functional Analysis: The Theory of Density-Corrected DFT

   https://doi.org/10.1021/acs.jctc.9b00826  

   Vuckovic, Stefan; Song, Suhwan; Kozlowski, John; Sim, Eunji; Burke, Kieron (October 2019, Journal of Chemical Theory and Computation)
2. Comparison of Density-Matrix Corrections to Density Functional Theory

   https://doi.org/10.1021/acs.jctc.2c00625  

   Gibney, Daniel; Boyn, Jan-Niklas; Mazziotti, David A. (November 2022, Journal of Chemical Theory and Computation)
3. Decomposition of the Electronic Energy in Terms of Density, Density Coherence, and the Connected Part of the Two-Body Reduced Density Matrix

   https://doi.org/10.1021/acs.jctc.1c00679  

   Zhang, Dayou; Truhlar, Donald G. (September 2021, Journal of Chemical Theory and Computation)
4. Comparison of a Neutral Density Model With the SET HASDM Density Database

   https://doi.org/10.1029/2021SW002888  

   Weimer, Daniel R.; Tobiska, W. Kent; Mehta, Piyush M.; Licata, R. J.; Drob, Douglas P.; Yoshii, Jean (December 2021, Space Weather)

   Abstract The EXospheric TEMperatures on a PoLyhedrAl gRid (EXTEMPLAR) method predicts the neutral densities in the thermosphere. The performance of this model has been evaluated through a comparison with the Air Force High Accuracy Satellite Drag Model (HASDM). The Space Environment Technologies (SET) HASDM database that was used for this test spans the 20 years 2000 through 2019, containing densities at 3 hr time intervals at 25 km altitude steps, and a spatial resolution of 10° latitude by 15° longitude. The upgraded EXTEMPLAR that was tested uses the newer Naval Research Laboratory MSIS 2.0 model to convert global exospheric temperature values to neutral density as a function of altitude. The revision also incorporated time delays that varied as a function of location, between the total Poynting flux in the polar regions and the exospheric temperature response. The density values from both models were integrated on spherical shells at altitudes ranging from 200 to 800 km. These sums were compared as a function of time. The results show an excellent agreement at temporal scales ranging from hours to years. The EXTEMPLAR model performs best at altitudes of 400 km and above, where geomagnetic storms produce the largest relative changes in neutral density. In addition to providing an effective method to compare models that have very different spatial resolutions, the use of density totals at various altitudes presents a useful illustration of how the thermosphere behaves at different altitudes, on time scales ranging from hours to complete solar cycles. 

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5. Emergence of the temperature–density relation in the low-density intergalactic medium

   https://doi.org/10.1093/mnras/stae401  

   Wells, Alexandra; Robinson, David; Avestruz, Camille; Gnedin, Nickolay Y. (February 2024, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT We examine the evolution of the phase diagram of the low-density intergalactic medium during the Epoch of Reionization in simulation boxes with varying reionization histories from the Cosmic Reionization on Computers project. The probability density function (PDF) of gas temperature at fixed density exhibits two clear modes: a warm and a cold temperature mode, corresponding to the gas inside and outside of ionized bubbles. We find that the transition between the two modes is ‘universal’ in the sense that its timing is accurately parametrized by the value of the volume-weighted neutral fraction for any reionization history. This ‘universality’ is more complex than just a reflection of the fact that ionized gas is warm and neutral gas is cold: it holds for the transition at a fixed value of gas density, and gas at different densities transitions from the cold to the warm mode at different values of the neutral fraction, reflecting a non-trivial relationship between the ionization history and the evolving gas density PDF. Furthermore, the ‘emergence’ of the tight temperature–density relation in the warm mode is also approximately ‘universally’ controlled by the volume-weighted neutral fraction for any reionization history. In particular, the ‘emergence’ of the temperature–density relation (as quantified by the rapid decrease in its width) occurs when the neutral fraction is 10−4 ≲ XH i ≲ 10−3 for any reionization history. Our results indicate that the neutral fraction is a primary quantity controlling the various properties of the temperature–density relation, regardless of reionization history. 

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