SPRING V0: Difference between revisions

Latest revision as of 06:58, 24 April 2023

SPRING_V0 = [real (array)]

Default: SPRING_V0 = 0 for all coordinates with status=8 in ICONST.

Description: Rate at which the bias potential is shifted in $uc/fs$ .

Consider the bias potential for a molecular-dynamics (MD) run of the form:

{\tilde {V}}(\xi _{1},\dots ,\xi _{M_{8}})=\sum _{\mu =1}^{M_{8}}{\frac {1}{2}}\kappa _{\mu }(\xi _{\mu }(q)-\xi _{0\mu })^{2},\;

where the sum runs over all ( $M_{8}$ ) coordinates the potential acts upon ( $\xi _{\mu }(q)$ ). The coordinates are defined in the ICONST file by setting the status=8. Optionally, the position of minimum ( $\xi _{0\mu }$ ) can be shifted at a constant rate ${\dot {\xi }}_{\mu }$ every MD step, i.e.,

\xi _{0\mu }(t+\Delta t)=\xi _{0\mu }(t)+{\dot {\xi }}_{\mu }(q)\Delta t,\;

where $\Delta t$ is the time step used in MD (POTIM). The rate ${\dot {\xi }}_{\mu }$ can be defined via the parameter SPRING_V0 and its units are $uc/fs$ , where $uc$ corresponds to the units of the coordinate the potential acts upon (e.g., ${\mathrm {\AA} }$ for coordinates with flag R, $rad.$ for coordinates with flag A, dimensionless for coordinates with flag W, etc...). The number of items defined via SPRING_V0 must be equal to $M_{8}$ , otherwise the calculation terminates with an error message.

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:SPRING_V0}}
 {{TAGDEF|SPRING_V0|[real (array)]}}
+{{DEF|SPRING_V0|0|for all coordinates with <code>status{{=}}8</code> in {{FILE|ICONST}}.}}
-Description: Consider the bias potential of the form:
+Description: Rate at which the bias potential is shifted in <math>uc/fs</math>.
-<math>
+----
-\tilde{V}(\xi_1,\dots,\xi_{M_8}) = \sum_{\mu=1}^{M}\frac{1}{2}\kappa_{\mu} (\xi_{\mu}(q)-\xi_{0\mu})^2 \;
+Consider the bias potential for a [[:Category:Molecular dynamics|molecular-dynamics]] (MD) run of the form:
+::<math>
+\tilde{V}(\xi_1,\dots,\xi_{M_8}) = \sum_{\mu=1}^{M_8}\frac{1}{2}\kappa_{\mu} (\xi_{\mu}(q)-\xi_{0\mu})^2, \;
 </math>
-where the sum runs over all (<math>M_8</math>) coordinates  the potential acts upon (<math>\xi_{\mu}(q)</math>), which are defined in the {{FILE|ICONST}}-file by setting the status to 8.
-Optionally, the position of minimum (<math>\xi_{0\mu}</math>) can be shifted at a constant rate <math>\dot{\xi}_{\mu}</math>, i.e.
-<math>
-\xi_{0\mu}(t+\Delta t) = \xi_{0\mu}(t)\dot{\xi}_{\mu}(q) \;
-</math>
+where the sum runs over all (<math>M_8</math>) coordinates the potential acts upon (<math>\xi_{\mu}(q)</math>). The coordinates are defined in the {{FILE|ICONST}} file by setting the <code>status=8</code>.
+Optionally, the position of minimum (<math>\xi_{0\mu}</math>) can be shifted at a constant rate <math>\dot{\xi}_{\mu}</math> every MD step, i.e.,
-The parameter {{TAG|SPRING_V0}} defines the rate at which the position of minimum (<math>\xi_{0\mu}</math>) of the harmonic bias potential of the form:
+::<math>
-<math>
+\xi_{0\mu}(t+\Delta t) = \xi_{0\mu}(t) + \dot{\xi}_{\mu}(q)\Delta t, \;
-\tilde{V}(\xi_1,\dots,\xi_{M_8}) = \sum_{\mu=1}^{M}\frac{1}{2}\kappa_{\mu} (\xi_{\mu}(q)-\xi_{0\mu})^2 \;
 </math>
-is shifted,
-where the sum runs over all (<math>M_8</math>) coordinates  the potential acts upon (<math>\xi_{\mu}(q)</math>), which are defined in the {{FILE|ICONST}}-file by setting the status to 8.
+where <math>\Delta t</math> is the time step used in MD ({{TAG|POTIM}}).
-The units of {{TAG|SPRING_V0}} are <math>uc/fs</math>, where <math>uc</math> corresponds to the units of the coordinate the potential acts upon (e.g., <math>{\AA}</math> for coordinates with <code>flag</code> R, <math>rad.</math> for coordinates with <code>flag</code> A, dimensionless for coordinates with <code>flag</code> W, etc...).
+The rate <math>\dot{\xi}_{\mu}</math> can be defined via the parameter {{TAG|SPRING_V0}} and its units are <math>uc/fs</math>, where <math>uc</math> corresponds to the units of the coordinate the potential acts upon (e.g., <math>{\AA}</math> for coordinates with <code>flag</code> R, <math>rad.</math> for coordinates with <code>flag</code> A, dimensionless for coordinates with <code>flag</code> W, etc...).
 The number of items defined via {{TAG|SPRING_V0}} must be equal to <math>M_8</math>, otherwise the calculation terminates with an error message.
 == Related tags and articles ==
-{{TAG|SPRING_K}}
+{{TAG|SPRING_K}},
-{{TAG|SPRING_R0}}
+{{TAG|SPRING_R0}},
-{{FILE|ICONST}}
+{{FILE|ICONST}},
 {{TAG|Biased molecular dynamics}}
+----
+[[Category:Molecular dynamics]][[Category:Biased molecular dynamics]]