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1. Can the Hartree–Fock kinetic energy exceed the exact kinetic energy?

   https://doi.org/10.1063/5.0105684  

   Crisostomo, S.; Levy, M.; Burke, K. (October 2022, The Journal of Chemical Physics)

   The Hartree–Fock (HF) approximation has been an important tool for quantum-chemical calculations since its earliest appearance in the late 1920s and remains the starting point of most single-reference methods in use today. Intuition suggests that the HF kinetic energy should not exceed the exact kinetic energy; but no proof of this conjecture exists, despite a near century of development. Beginning from a generalized virial theorem derived from scaling considerations, we derive a general expression for the kinetic energy difference that applies to all systems. For any atom or ion, this trivially reduces to the well-known result that the total energy is the negative of the kinetic energy and, since correlation energies are never positive, proves the conjecture in this case. Similar considerations apply to molecules at their equilibrium bond lengths. We use highly precise calculations on Hooke’s atom (two electrons in a parabolic well) to test the conjecture in a nontrivial case and to parameterize the difference between density functional and HF quantities, but find no violations of the conjecture. 

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2. Unveiling hidden energy poverty using the energy equity gap

   https://doi.org/10.1038/s41467-022-30146-5  

   Cong, Shuchen; Nock, Destenie; Qiu, Yueming Lucy; Xing, Bo (May 2022, Nature Communications)

   Abstract Income-based energy poverty metrics ignore people’s behavior patterns, particularly reducing energy consumption to limit financial stress. We investigate energy-limiting behavior in low-income households using a residential electricity consumption dataset. We first determine the outdoor temperature at which households start using cooling systems, the inflection temperature. Our relative energy poverty metric, theenergy equity gap, is defined as the difference in the inflection temperatures between low and high-income groups. In our study region, we estimate the energy equity gap to be between 4.7–7.5 °F (2.6–4.2 °C). Within a sample of 4577 households, we found 86 energy-poor and 214 energy-insecure households. In contrast, the income-based energy poverty metric, energy burden (10% threshold), identified 141 households as energy-insecure. Only three households overlap between our energy equity gap and the income-based measure. Thus, the energy equity gap reveals a hidden but complementary aspect of energy poverty and insecurity. 

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3. Energy Transition, Distributed Energy Resources, and the Need for Information

   Unel, Burcin; Bialek, Sylwia; Kim, Jip; Dvorkin, Yury (January 2020, IAEE energy forum)
4. The impact of mandatory energy audits on building energy use

   https://doi.org/10.1038/s41560-020-0589-6  

   Kontokosta, Constantine E.; Spiegel-Feld, Danielle; Papadopoulos, Sokratis (April 2020, Nature Energy)

   null (Ed.)
5. Hydrogen energy levels from the anomalous energy-momentum QED trace

   https://doi.org/10.1103/PhysRevD.110.076020  

   Eides, Michael I (October 2024, Physical Review D)

   Energy levels of hydrogen are calculated as one-loop matrix elements of the QED energy-momentum tensor trace in the external field approximation. An explicit connection established between the one-loop trace diagrams and the standard Lamb shift one-loop diagrams. Our calculations provide an argument against inclusion of the anomalous trace contribution as a separate term in the decomposition of the QED quantum field Hamiltonian and serve as an illustration how the trace anomaly is realized in the bound state QED. 

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