Orbital-free density functional theory: Differences and similarities between electronic and nuclear systems

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The total energy can be written in a useful form by exploiting the fact that

1 ∂ρ

∇ ρ= √ ∇ρ=

er .

2 ρ

2ρ ∂r

In this way,

 

 2 2/3 5/3

1 ∂ρ 2

δV

2

2

3 3

3π

E =β

d r

+α

d r

ρ + d 3r

2m

4ρ ∂r

2m

δρ

 2

 2 2/3 5/3

δV

∂ρ

2

2

2 1

23

ρ.

3π

d r 4π r

+α

d r 4π r

ρ + dr 4π r2

=β

2m

4ρ ∂r

2m

δρ

PTEP 2023, 103D01

G. Colò and K. Hagino

© The Author(s) 2023. Published by Oxford University Press on behalf of the Physical Society of Japan. This is an Open Access article distributed under the terms of the Creative

Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work

is properly cited.

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