Explicit corrections to the gradient expansion for the kinetic energy in one dimension

2019/09/11 by Kieron Burke, Burke, Kieron
Chemistry · Physics and Astronomy · #Advanced Chemical Physics Studies #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Fullerene Chemistry and Applications #Materials Science (cond-mat.mtrl-sci) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum, superfluid, helium dynamics

paper · pdf · doi:10.48550/arxiv.1909.10320

openalex publication_date 2019/09/11 · openalex created_date 2019/09/26 · openalex updated_date 2026/07/28

Abstract

A mathematical framework is constructed for the sum of the lowest N eigenvalues of a potential. Exactness is illustrated on several model systems (harmonic oscillator, particle in a box, and Poschl-Teller well). Its order-by-order semiclassical expansion reduces to the gradient expansion for slowly-varying densities, but also yields a correction when the system is finite and the spectrum discrete. Some singularities can be avoided when evaluating the correction to the leading term. Explicit corrections to the gradient expansion to the kinetic energy in one dimension are found which, in simple cases, greatly improve accuracy. We discuss the relevance to practical density functional calculations.

Related

• Convergent sum of gradient expansion of the kinetic-energy density functional up to the sixth order term using Pade approximant
• A new Green's function formalism for kinetic energy density functional for atomic and molecular system: Emergence of N-dependence using model potentials
• Scaling of the known exact explicit forms of the non-interacting kinetic-energy density functional
• Correction to kinetic energy density using exactly solvable model
• Generalized gradient approximations to density functional theory: comparison with exact results