Molecular Dynamics Chapter 2. Molecular Dynamics in Various ...
Molecular Dynamics Chapter 2. Molecular Dynamics in Various ...
Molecular Dynamics Chapter 2. Molecular Dynamics in Various ...
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<strong>Molecular</strong> <strong>Dynamics</strong> <strong>Chapter</strong> <strong>2.</strong>1<br />
Extended Hamiltonian to Realize Grand Canonical Ensemble<br />
One particle scheme:<br />
H<br />
extended<br />
1 dsr<br />
= H<br />
o<br />
( n −1)<br />
+ M<br />
r<br />
+ srU<br />
o<br />
− srμ + μ<br />
2 dt<br />
2<br />
0≤ S r<br />
≤1<br />
Nonl<strong>in</strong>ear switch<strong>in</strong>g S r<br />
U o<br />
Orig<strong>in</strong>al Lennard-Jones <strong>in</strong>teraction:<br />
Nonl<strong>in</strong>ear Switch<strong>in</strong>g (Softcore potential):<br />
⎡ A B<br />
ε ⎢ 12<br />
− 6<br />
⎣r<br />
r<br />
⎤<br />
⎥<br />
⎦<br />
s<br />
r<br />
⎧ ⎡<br />
⎨ε<br />
⎢<br />
⎩ ⎣<br />
A<br />
+ σ (1 −<br />
−<br />
B<br />
+ σ (1 −<br />
2<br />
6 2<br />
( r sr<br />
)) ( r sr<br />
))<br />
3<br />
⎤⎫<br />
⎥⎬<br />
⎦⎭