Reformulation of density functional theory for N-representable densities and the resolution of the v-representability problem |
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| Affiliation: | 1. Physical and Life Sciences, Lawrence Livermore National Laboratory, PO Box 808, L-372, Livermore, CA 94551, United States;2. Department of Physics and the Quantum Theory Project, University of Florida, Gainesville, FL 32611, United States;3. Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States;4. Department of Physics, University of North Carolina Asheville, Asheville, NC 28804 , United States;1. Department of Physics, Science, Khon Kaen University, Khon Kaen, 40002, Thailand;2. Integrated Nanotechnology Research Center (INRC), Department of Physics, Science, Khon Kaen University, Khon Kaen, 40002, Thailand;3. School of Physics, Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand;4. School of Electronic and Electrical Engineering, University of Leeds, Leeds, UK;1. Laboratoire Collisions, Agrégats, Réactivité, UMR 5589, IRSAMC, Université Paul Sabatier, F-31062 Toulouse, France;2. Laboratoire de Chimie Physique, Bât 349, Univ Paris-Sud, UMR 8000, Université Paris Saclay, F-91405 Orsay, France;3. Département de Chimie, Université de Liège, Sart Tilman, B6, B-4000 Liège, Belgium;1. Department of Structures and Civil Engineering, University Malaya, 50603 Kuala Lumpur, Malaysia;2. School of Engineering, Griffith University, Gold Coast Campus, Southport 4222, Australia;3. School of Engineering, The University of Newcastle, Callaghan, New South Wales 2308, Australia;1. Department of Theoretical Physics, University of Science, Ho Chi Minh City 700000, Viet Nam;2. Vietnam National University, Ho Chi Minh City 700000, Viet Nam;3. Department of Physics, Ho Chi Minh City University of Education, Ho Chi Minh City, Viet Nam;4. Department of Natural Science, Dong Nai University, Dong Nai, Viet Nam;5. Industrial University of Ho Chi Minh City, Go Vap District, Ho Chi Minh City, Viet Nam;6. Laboratory of Applied Physics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Viet Nam;7. Faculty of Technology, Van Lang University, Ho Chi Minh City, Viet Nam;8. Light-Matter Interactions for Quantum Technologies Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan;9. International Cooperation Office, Ho Chi Minh City University of Education, Ho Chi Minh City, Viet Nam |
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| Abstract: | Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide proof of existence of a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of the density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism. Numerical results for one-dimensional non-interacting systems illustrate the formalism. Some direct formal and practical implications of the present reformulation of DFT are also discussed. |
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| Keywords: | C. Ab initio calculations D. Electronic structure |
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