Sixth-order term of the gradient expansion of the kinetic-energy density functional
Sixth-order term of the gradient expansion of the kinetic-energy density functional
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动能密度泛函梯度展开的六阶项
DOI：
10.1103/physreva.24.1682
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发表时间：
1981
影响因子：
2.9
通讯作者：
D. R. Murphy
中科院分区：
文献类型：
--
作者：
D. R. Murphy
Hodges的方法获得的梯度展开的推广推导，然后用来确定六阶项。其公式如下：T 6 [ρ]=（3 π 2）− 413 45 360 π ρ− 1 3 [13（2 ρ ρ）2+ 2575 144（2 ρ ρ）3+ 249 16（ρ ρ）2（4 ρ ρ）+ 1499 18（ρ ρ）2（2 ρ ρ）2− 1307 36（ρ ρ）2（→ ρ·→ 2 ρ ρ 2）+ 343 18（→ ρ·→ → ρ ρ 2）2+ 8341 7 2（2 ρ ρ）（ρ ρ）4− 1 600 495 2592（ρ ρ）6] d 3 r.对于原子密度，T6 [ρ]在原子核附近和很远的地方是发散的。
A generalization of Hodges's method of obtaining the gradient expansion is derived and then employed to determine the sixth-order term. The formula for it is as follows: T 6 [ρ]=(3 π 2)− 413 45 360∫ ρ− 1 3 [13 (∇∇ 2 ρ ρ) 2+ 2575 144 (∇ 2 ρ ρ) 3+ 249 16 (∇ ρ ρ) 2 (∇ 4 ρ ρ)+ 1499 18 (∇ ρ ρ) 2 (∇ 2 ρ ρ) 2− 1307 36 (∇ ρ ρ) 2 (∇→ ρ·∇→∇ 2 ρ ρ 2)+ 343 18 (∇→ ρ·∇→∇→ ρ ρ 2) 2+ 8341 7 2 (∇ 2 ρ ρ)(∇ ρ ρ) 4− 1 600 495 2592 (∇ ρ ρ) 6] d 3 r. For atomic densities, T 6 [ρ] is divergent near the nucleus and at large distances.