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dihedral_class2.tex
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Sat, Nov 2, 07:21
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text/x-tex
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Mon, Nov 4, 07:21 (2 d)
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rLAMMPS lammps
dihedral_class2.tex
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\documentclass
[12pt]
{
article
}
\begin
{
document
}
\begin
{
eqnarray*
}
E
&
=
&
E
_
d + E
_{
mbt
}
+ E
_{
ebt
}
+ E
_{
at
}
+ E
_{
aat
}
+ E
_{
bb13
}
\\
E
_
d
&
=
&
\sum
_{
n=1
}^{
3
}
K
_
n [ 1 -
\cos
(n
\phi
-
\phi
_
n) ]
\\
E
_{
mbt
}
&
=
&
(r
_{
jk
}
- r
_
2) [ A
_
1
\cos
(
\phi
) + A
_
2
\cos
(2
\phi
) + A
_
3
\cos
(3
\phi
) ]
\\
E
_{
ebt
}
&
=
&
(r
_{
ij
}
- r
_
1) [ B
_
1
\cos
(
\phi
) + B
_
2
\cos
(2
\phi
) + B
_
3
\cos
(3
\phi
) ] +
\\
&
&
(r
_{
kl
}
- r
_
3) [ C
_
1
\cos
(
\phi
) + C
_
2
\cos
(2
\phi
) + C
_
3
\cos
(3
\phi
) ]
\\
E
_{
at
}
&
=
&
(
\theta
_{
ijk
}
-
\theta
_
1) [ D
_
1
\cos
(
\phi
) + D
_
2
\cos
(2
\phi
) + D
_
3
\cos
(3
\phi
) ] +
\\
&
&
(
\theta
_{
jkl
}
-
\theta
_
2) [ E
_
1
\cos
(
\phi
) + E
_
2
\cos
(2
\phi
) + E
_
3
\cos
(3
\phi
) ]
\\
E
_{
aat
}
&
=
&
M (
\theta
_{
ijk
}
-
\theta
_
1) (
\theta
_{
jkl
}
-
\theta
_
2)
\cos
(
\phi
)
\\
E
_{
bb13
}
&
=
&
N (r
_{
ij
}
- r
_
1) (r
_{
kl
}
- r
_
3)
\end
{
eqnarray*
}
\end
{
document
}
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