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Commit abfc109c authored by Omar Valsson's avatar Omar Valsson
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Merge remote-tracking branch 'origin/v2.4' into v2.4-ves

parents c32f536e 7c14f705
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...@@ -45,7 +45,7 @@ often cheaper and easier to calculate the distances between all the pairs of ato ...@@ -45,7 +45,7 @@ often cheaper and easier to calculate the distances between all the pairs of ato
between the two structures, \f$\mathbf{X}^a\f$ and \f$\mathbf{X}^b\f$ can then be measured as: between the two structures, \f$\mathbf{X}^a\f$ and \f$\mathbf{X}^b\f$ can then be measured as:
\f[ \f[
d(\mathbf{X}^A, \mathbf{X}^B) = \frac{1}{N(N-1)} \sum_{i \ne j} [ d(\mathbf{x}_i^a,\mathbf{x}_j^a) - d(\mathbf{x}_i^b,\mathbf{x}_j^b) ]^2 d(\mathbf{X}^A, \mathbf{X}^B) = \sqrt{\frac{1}{N(N-1)} \sum_{i \ne j} [ d(\mathbf{x}_i^a,\mathbf{x}_j^a) - d(\mathbf{x}_i^b,\mathbf{x}_j^b) ]^2}
\f] \f]
where \f$N\f$ is the number of atoms and \f$d(\mathbf{x}_i,\mathbf{x}_j)\f$ represents the distance between where \f$N\f$ is the number of atoms and \f$d(\mathbf{x}_i,\mathbf{x}_j)\f$ represents the distance between
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...@@ -55,12 +55,13 @@ eRMSD measures the distance between structures by considering only the relative ...@@ -55,12 +55,13 @@ eRMSD measures the distance between structures by considering only the relative
2. Calculate all pairwise distance vectors \f$ \vec{r}_{i,j} \f$ among base centers. 2. Calculate all pairwise distance vectors \f$ \vec{r}_{i,j} \f$ among base centers.
3. Rescale distance vectors as \f$ \tilde{\vec{r}}_{i,j} = (r_x/a,r_y/a,r_z/b) \f$, where \f$ a=b=5 \AA, c= 3 \AA\f$. This rescaling has the effect of weghting more deviations on the z-axis with respect to the x/y directions. 3. Rescale distance vectors as \f$ \tilde{\vec{r}}_{i,j} = (r_x/a,r_y/a,r_z/b) \f$, where a=b=5 \AA, c= 3 \AA. This rescaling has the effect of weghting more deviations on the z-axis with respect to the x/y directions.
4. Calculate the G vectors 4. Calculate the G vectors
\f[ \f[
\vec{G}(\tilde{\vec{r}}) = (\sin(\gamma \tilde{r}) \tilde{r}_x/\tilde{r},\sin(\gamma \tilde{r}) \tilde{r}_y/\tilde{r},\sin(\gamma \tilde{r}) \tilde{r}_z/\tilde{r}, 1+\cos(\gamma \tilde{r})) \times \Theta(\tilde{r}_{cutoff}-\tilde{r}) \vec{G}(\tilde{\vec{r}}) = (\sin(\gamma \tilde{r}) \tilde{r}_x/\tilde{r},\sin(\gamma \tilde{r}) \tilde{r}_y/\tilde{r},\sin(\gamma \tilde{r}) \tilde{r}_z/\tilde{r}, 1+\cos(\gamma \tilde{r})) \times
\frac{\Theta(\tilde{r}_{cutoff}-\tilde{r})}{\gamma}
\f] \f]
Here, \f$ \gamma = \pi/\tilde{r}_{cutoff}\f$ and \f$ \Theta \f$ is the Heaviside step function. The default cutoff is set to 2.4. Here, \f$ \gamma = \pi/\tilde{r}_{cutoff}\f$ and \f$ \Theta \f$ is the Heaviside step function. The default cutoff is set to 2.4.
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...@@ -22,7 +22,7 @@ In PT, exchanges are usually attempted between adjacent temperatures ...@@ -22,7 +22,7 @@ In PT, exchanges are usually attempted between adjacent temperatures
with the following acceptance probability: with the following acceptance probability:
\f[ \f[
p(i \rightarrow j) = min \{ 1,\Delta_{i,j}^{PT} \}, p(i \rightarrow j) = min \{ 1,e^{\Delta_{i,j}^{PT}} \},
\f] \f]
with with
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