Theor Chem Acc (2015) 134:117
1 3
(2)
S o =
⎛
⎝
x 2 o xy o xz o
y 2 o yz o
z 2 o
⎞
⎠
(3)
Q
+ S o Q = S
o
(4)
S
o =
⎛
⎜
⎝
x 2 o 0
0
y 2 o 0
z 2 o
⎞
⎟
⎠
(5)
V o =
4π
3
S
o
x S
o
y S
o
z
(6)
r A =
W A (r) ρ(r) r dr
(7)
r
2
A =
W A (r) ρ(r) r
2 dr
3 Results and discussion
3.1 Radial density
3.1.1 Atomic radial density
The atomic radial density of hydrogen, fl uorine, and chlorine is shown in Fig. 1 to illustrate shell structure and electron distribution. The 2D, 3D, contour, and gradient paths
of radial density are shown for each atom. The plots reveal
that H, F, and Cl have one, two, and three shells, respectively, which matches their period position. An atomic shell
is defi ned here as the region of space bounded between
(8)
r A−B =
W A (r) W B (r) ρ(r) r dr
(9)
r
2
A−B =
W A (r) W B (r) ρ(r) r
2 dr
Fig. 1 The 2D ( ρ rad vs. x ) , 3D ( ρ rad vs. x , y ) contour ( ρ rad vs. x , y ), and gradient path ( ∇ρ rad vs. x , y ) plots for the H, F, and Cl atoms
59
Reprinted from the journal
1 3
(2)
S o =
⎛
⎝
x 2 o xy o xz o
y 2 o yz o
z 2 o
⎞
⎠
(3)
Q
+ S o Q = S
o
(4)
S
o =
⎛
⎜
⎝
x 2 o 0
0
y 2 o 0
z 2 o
⎞
⎟
⎠
(5)
V o =
4π
3
S
o
x S
o
y S
o
z
(6)
r A =
W A (r) ρ(r) r dr
(7)
r
2
A =
W A (r) ρ(r) r
2 dr
3 Results and discussion
3.1 Radial density
3.1.1 Atomic radial density
The atomic radial density of hydrogen, fl uorine, and chlorine is shown in Fig. 1 to illustrate shell structure and electron distribution. The 2D, 3D, contour, and gradient paths
of radial density are shown for each atom. The plots reveal
that H, F, and Cl have one, two, and three shells, respectively, which matches their period position. An atomic shell
is defi ned here as the region of space bounded between
(8)
r A−B =
W A (r) W B (r) ρ(r) r dr
(9)
r
2
A−B =
W A (r) W B (r) ρ(r) r
2 dr
Fig. 1 The 2D ( ρ rad vs. x ) , 3D ( ρ rad vs. x , y ) contour ( ρ rad vs. x , y ), and gradient path ( ∇ρ rad vs. x , y ) plots for the H, F, and Cl atoms
59
Reprinted from the journal