Leading corrections to the local density approximation of the kinetic energy in one dimension (bibtex)

by Kieron Burke

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 PoschlTeller well). Its order-by-order semiclassical expansion reduces to the gradient expansion for slowlyvarying 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.

Reference:

Leading corrections to the local density approximation of the kinetic energy in one dimension Kieron Burke, J. Chem. Phys. 152, (2020).

Bibtex Entry:

@article{B20, Pub-num = {195}, Title = {Leading corrections to the local density approximation of the kinetic energy in one dimension}, Author = {Kieron Burke}, 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 PoschlTeller well). Its order-by-order semiclassical expansion reduces to the gradient expansion for slowlyvarying 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.}, Doi = {10.1063/5.0002287}, %% Issn = {}, Year = {2020}, Month = {February}, Journal = {J. Chem. Phys.}, Volume = {152}, Issue = {8}, %% Number = {}, %% Pages = {}, Publisher = {American Institute of Physics}, Url = {https://aip.scitation.org/doi/10.1063/5.0002287}, arXiv = {1909.10320v1}, %% keywords = {} %%}

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