Lennard-Jones-Potential
U
L
J
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r
)
=
4
ϵ
[
(
σ
r
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12
−
(
σ
r
)
6
]
F
L
J
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−
d
U
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r
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d
r
=
4
ϵ
σ
[
12
(
σ
r
)
13
−
6
(
σ
r
)
7
]
\begin{aligned} U_\mathrm{LJ}(r) & = 4\epsilon \left[ \left( \frac{\sigma}{r} \right)^{12} - \left( \frac{\sigma}{r} \right)^{6} \right] \\ F_\mathrm{LJ}(r) = -\frac{\mathrm{d} U(r)}{\mathrm{d}r} & = \frac{4\epsilon}{\sigma} \left[ 12 \left( \frac{\sigma}{r} \right)^{13} - 6 \left( \frac{\sigma}{r} \right)^{7} \right] \\ \end{aligned}
U
LJ
(
r
)
F
LJ
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r
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=
−
d
r
d
U
(
r
)
=
4
ϵ
[
(
r
σ
)
12
−
(
r
σ
)
6
]
=
σ
4
ϵ
[
12
(
r
σ
)
13
−
6
(
r
σ
)
7
]
r
r
r
y
y
y
y
=
U
L
J
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r
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\;y = U_\mathrm{LJ}(r)
y
=
U
LJ
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r
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y
=
F
L
J
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r
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\;y = F_\mathrm{LJ}(r)
y
=
F
LJ
(
r
)
0.5
1.0
1.5
2.0
2.5
3.0
−2.0
0.0
2.0
−3.0
−2.5
−1.5
−1.0
−0.5
0.5
1.0
1.5
2.5
3.0
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σ
\sigma
σ
1
ϵ
\epsilon
ϵ
1
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F
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r
)
F(r)
F
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r
)
Reset