Editing Flexible molecules
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Latest revision | Your text | ||
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== Bond distances == | == Bond distances == | ||
Atoms linked by a chemical bond (stretching) | * Atoms linked by a chemical bond (stretching): | ||
<math> V_{str} (r_{12}) = \frac{1}{2} K_{str} ( r_{12} - b_0 )^2 </math> | |||
== Bond Angles == | == Bond Angles == | ||
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Bond sequence: 1-2-3: | Bond sequence: 1-2-3: | ||
Bond Angle: <math> | Bond Angle: <math> \theta </math> | ||
<math> \cos \theta = \frac{ \vec{r}_{21} \cdot \vec{r}_{23} } {|\vec{r}_{21}| |\vec{r}_{23}|} | |||
</math> | </math> | ||
Two typical forms are used to model the ''bending'' potential: | Two typical forms are used to model the ''bending'' potential: | ||
<math> | |||
V_{bend}(\theta) = \frac{1}{2} k_{\theta} \left( \theta - \theta_0 \right)^2 | |||
</math> | </math> | ||
<math> | |||
V_{bend}(\cos \theta) = \frac{1}{2} k_{c} \left( \cos \theta - c_0 \right)^2 | |||
</math> | </math> | ||
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Bond sequence: 1-2-3-4 | Bond sequence: 1-2-3-4 | ||
Dihedral angle (<math> | Dihedral angle (<math> \phi </math>) definition: | ||
Consider the following vectors: | Consider the following vectors: | ||
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*<math> \vec{c} = \vec{a} \times \vec{b} </math> | *<math> \vec{c} = \vec{a} \times \vec{b} </math> | ||
*<math> e_{34} = (\cos \phi) \vec{a} + ( | *<math> e_{34} = (\cos \phi) \vec{a} + (sin \phi) \vec{c} </math> | ||
For molecules with internal rotation degrees of freedom (e.g. ''n''-alkanes), a ''torsional'' potential is | For molecules with internal rotation degrees of freedom (e.g. ''n''-alkanes), a ''torsional'' potential is | ||
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*<math> | *<math> | ||
V_{tors} \left(\phi\right) = \sum_{i=0}^n a_i \left( \cos \phi \right)^i | |||
</math> | </math> | ||
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* <math> | * <math> | ||
V_{tors} \left(\phi\right) = \sum_{i=0}^n b_i \cos \left( i \phi \right) | |||
</math> | </math> | ||