Flexible molecules - Revision history

Carl McBride at 14:32, 30 July 2007

2007-07-30T14:32:02Z

← Older revision		Revision as of 16:32, 30 July 2007
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	== Bond distances ==		== Bond distances ==
	Atoms linked by a chemical bond (stretching):		Atoms linked by a chemical bond (stretching) using the [[harmonic spring approximation]]:

	<math> \Phi_{str} (r_{12}) = \frac{1}{2} K_{str} ( r_{12} - b_0 )^2 </math>		:<math> \Phi_{str} (r_{12}) = \frac{1}{2} K_{str} ( r_{12} - b_0 )^2 </math>

	However, this internal coordinates are very often kept constrained (fixed bond distances)		However, this internal coordinates are very often kept constrained (fixed bond distances)
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	Bond Angle: <math> \left. \theta \right. </math>		Bond Angle: <math> \left. \theta \right. </math>

	<math> \cos \theta = \frac{ \vec{r}_{21} \cdot \vec{r}_{23} } {\|\vec{r}_{21}\| \|\vec{r}_{23}\|}		:<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>		:<math>
	\Phi_{bend}(\theta) = \frac{1}{2} k_{\theta} \left( \theta - \theta_0 \right)^2		\Phi_{bend}(\theta) = \frac{1}{2} k_{\theta} \left( \theta - \theta_0 \right)^2
	</math>		</math>

	<math>		:<math>
	\Phi_{bend}(\cos \theta) = \frac{1}{2} k_{c} \left( \cos \theta - c_0 \right)^2		\Phi_{bend}(\cos \theta) = \frac{1}{2} k_{c} \left( \cos \theta - c_0 \right)^2
	</math>		</math>

2007-07-05T11:11:35Z

Reverted edits by 222.66.97.75 (Talk); changed back to last version by Nice and Tidy

← Older revision		Revision as of 13:11, 5 July 2007
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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} (\sin \phi) \vec{c} </math>		*<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

2007-07-04T20:19:54Z

← Older revision		Revision as of 22:19, 4 July 2007
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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} + (\sin \phi) \vec{c} </math>		*<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

2007-06-21T13:06:59Z

← Older revision		Revision as of 15:06, 21 June 2007
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	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>		<math> \Phi_{str} (r_{12}) = \frac{1}{2} K_{str} ( r_{12} - b_0 )^2 </math>

	However, this internal coordinates are very often kept constrained (fixed bond distances)		However, this internal coordinates are very often kept constrained (fixed bond distances)
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	<math>		<math>
	V_{bend}(\theta) = \frac{1}{2} k_{\theta} \left( \theta - \theta_0 \right)^2		\Phi_{bend}(\theta) = \frac{1}{2} k_{\theta} \left( \theta - \theta_0 \right)^2
	</math>		</math>

	<math>		<math>
	V_{bend}(\cos \theta) = \frac{1}{2} k_{c} \left( \cos \theta - c_0 \right)^2		\Phi_{bend}(\cos \theta) = \frac{1}{2} k_{c} \left( \cos \theta - c_0 \right)^2
	</math>		</math>

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	*<math>		*<math>
	V_{tors} \left(\phi\right) = \sum_{i=0}^n a_i \left( \cos \phi \right)^i		\Phi_{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)		\Phi_{tors} \left(\phi\right) = \sum_{i=0}^n b_i \cos \left( i \phi \right)
	</math>		</math>

2007-05-25T16:30:55Z

← Older revision		Revision as of 18:30, 25 May 2007
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	Pair interactions similar to the typical intermolecular potentials are frequently		Pair interactions similar to the typical intermolecular potentials are frequently
	used (e.g. [[Lennard-Jones model\|Lennard-Jones]] potentials)		used (e.g. [[Lennard-Jones model\|Lennard-Jones]] potentials)
			[[category: force fields]]
			[[category: models]]

2007-03-30T11:01:11Z

← Older revision	Revision as of 13:01, 30 March 2007
(No difference)

2007-03-19T11:26:09Z

Van der Waals intramolecular interactions

← Older revision		Revision as of 13:26, 19 March 2007
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	Pair interactions similar to the typical intermolecular potentials are frequently		Pair interactions similar to the typical intermolecular potentials are frequently
	used (e.g. [[Lennard-Jones]] potentials)		used (e.g. [[Lennard-Jones model\|Lennard-Jones]] potentials)

2007-02-26T14:56:22Z

Bond distances

← Older revision		Revision as of 16:56, 26 February 2007
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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>		<math> V_{str} (r_{12}) = \frac{1}{2} K_{str} ( r_{12} - b_0 )^2 </math>

2007-02-22T13:51:33Z

Van der Waals intramolecular interactions

← Older revision		Revision as of 15:51, 22 February 2007
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	== Van der Waals intramolecular interactions ==		== Van der Waals intramolecular interactions ==

	For pairs of atoms (or sites) which are separated by a certain number of chemical bonds,		For pairs of atoms (or sites) which are separated by a certain number of chemical bonds:
	~~pair interaction models~~ similar to the typical intermolecular potentials are frequently
			Pair interactions similar to the typical intermolecular potentials are frequently
	used (e.g. [[Lennard-Jones]] potentials)		used (e.g. [[Lennard-Jones]] potentials)

2007-02-22T11:51:25Z

Bond Angles

← Older revision		Revision as of 13:51, 22 February 2007
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	Bond sequence: 1-2-3:		Bond sequence: 1-2-3:

	Bond Angle: <math> \theta </math>		Bond Angle: <math> \left. \theta \right. </math>

	<math> \cos \theta = \frac{ \vec{r}_{21} \cdot \vec{r}_{23} } {\|\vec{r}_{21}\| \|\vec{r}_{23}\|}		<math> \cos \theta = \frac{ \vec{r}_{21} \cdot \vec{r}_{23} } {\|\vec{r}_{21}\| \|\vec{r}_{23}\|}