Merge remote-tracking branch 'upstream/develop' into mw_APIs_for_SOECP

docs/analyzing.rst

@@ -1457,32 +1457,44 @@ Usage examples
 Below are example use cases for the H2O molecule using DMC data.
 
 Plot DMC non-cumulative radial density of the O atom:
+
 ::
+
   qdens-radial -p -s O -r 1 dmc.s002.Density_q.xsf
 
 Plot DMC cumulative radial density of the O atom:
+
 ::
+
   qdens-radial -p -s O -r 1 -c dmc.s002.Density_q.xsf
 
 For the cumulative case, ``qdens-radial`` will also print the cumulative value at the specified radius, i.e., an estimate of the atomic occupation.
 
 Estimate of the DMC atomic occupation:
+
 ::
+
   qdens-radial -p -s O -r 1.1 -c dmc.s002.Density_q.xsf
 
 Output:
+
 ::
+
   Cumulative Value of O Species at Cutoff 1.1 is: 6.55517033828574
 
 
 One can also get an extrapolated estimate (mixed-estimator bias) for this quantity by providing a VMC ``.xsf`` file.
 
 Estimate of the extrapolated atomic occupation:
+
 ::
+
   qdens-radial -p -s O -r 1.1 -c --vmc=dmc.s000.Density_q.xsf dmc.s002.Density_q.xsf
   
 Output:
+
 ::
+
   Extrapolating from VMC and DMC densities...
   Cumulative Value of O Species at Cutoff 1.1 is: 6.576918233167152
 
@@ -1498,12 +1510,16 @@ to obtain the error bar on the occupation.
 3. Make sure the number of samples (``-n``) is converged.
 
 Estimate DMC atomic occupation with error bar:
+
 ::
+
   qdens-radial -p -s O -r 1.1 -c -n 20 --dmcerr=dmc.s002.Density_q+err.xsf dmc.s002.Density_q.xsf
 
 
 Output:
+
 ::
+
   Resampling to obtain error bar (NOTE: This can be slow)...
   Will compute 20 samples...
   ...

docs/lab_excited.rst

@@ -58,14 +58,14 @@ photoemission experiments. In contrast, the emission energy of a
 negatively charged system (or the energy required to convert a
 negatively charged system to a neutral system), known as electron
 affinity (EA), is available from inverse photoemission experiments.
-Outlines of these experiments are shown in :numref:`fig22`.
+Outlines of these experiments are shown in :numref:`fig22`, reproduced from :cite:`Onida2002a`.
 
 .. _fig22:
 .. figure:: /figs/lab_excited_experiments.png
   :width: 500
   :align: center
 
-  Direct and inverse photoemission experiments involve charged excitations, whereas optical absorption experiments involve excitations that are just enough to be excited to the conduction band. From :cite:`Onida2002a`
+  Direct and inverse photoemission experiments involve charged excitations, whereas optical absorption experiments involve excitations that are just enough to be excited to the conduction band. 
 
 Following the explanation in the previous paragraph and :numref:`fig22`, the *quasiparticle* band gap of a material can be defined as:
 

docs/methods.rst

@@ -1485,17 +1485,17 @@ Additional information:
 
 .. math::
 
-  E_\text{trial} = E_\text{pop_avg}+(\ln \texttt{targetwalkers}-\ln N_\text{pop}) / \texttt{timestep}
+  E_\text{trial} = E_\text{pop\_avg}+(\ln \texttt{targetwalkers}-\ln N_\text{pop}) / \texttt{timestep}
 
-where :math:`E_\text{pop_avg}` is the local energy average over the walker population at the current step
+where :math:`E_\text{pop\_avg}` is the local energy average over the walker population at the current step
 and :math:`N_\text{pop}` is the current walker population size.
 After the warm-up phase, the trial energy is updated as
 
 .. math::
 
   E_\text{trial} = E_\text{ref}+\texttt{feedback}\cdot(\ln\texttt{targetWalkers}-\ln N_\text{pop})
 
-where :math:`E_\text{ref}` is the :math:`E_\text{pop_avg}` average over all the post warm-up steps up to the current step. The update frequency is controlled by ``energyUpdateInterval``.
+where :math:`E_\text{ref}` is the :math:`E_\text{pop\_avg}` average over all the post warm-up steps up to the current step. The update frequency is controlled by ``energyUpdateInterval``.
 
 -  ``energyUpdateInterval``: Post warm-up, the trial energy is updated every
    ``energyUpdateInterval`` steps. Default value is 1 (every step).

docs/output_overview.rst

@@ -134,31 +134,28 @@ The .config.h5 file
 
 This file contains stored walker configurations.
 
-* GROUP "root"
-  * GROUP "state_0"
-    * DATASET "block"
-      * int
-      * SCALAR
-
-    * DATASET "number_of_walkers"
-      * size_t
-      * SCALAR
-
-    * DATASET "walker_partition"
-      * int
-      * ARRAY ( offsets )
-
-    * DATASET "walker_weights"
-      * double
-      * ARRAY ( weights )
-
-    * DATASET "walkers"
-      * double
-      * ARRAY ( configurations )
-
-  * DATASET "version"
-    * int
-    * ARRAY ( major version number, minor version number )
+::
+   
+   * GROUP "root"
+     * GROUP "state_0"
+       * DATASET "block"
+         * int
+         * SCALAR  
+       * DATASET "number_of_walkers"
+         * size_t
+         * SCALAR
+       * DATASET "walker_partition"
+         * int
+         * ARRAY ( offsets )
+       * DATASET "walker_weights"
+         * double
+         * ARRAY ( weights )
+       * DATASET "walkers"
+         * double
+         * ARRAY ( configurations )
+     * DATASET "version"
+       * int
+       * ARRAY ( major version number, minor version number )
 
 The .random.h5 file
 ~~~~~~~~~~~~~~~~~~~

docs/spin_orbit.rst

@@ -24,8 +24,8 @@ The single particle spinors used in QMCPACK take the form
 .. math::
   :label: seqn1
 
-    \phi(\mathbf{r},s) &=& \, \phi^\uparrow(\mathbf{r}) \chi^\uparrow(s) + \phi^{\downarrow}(\mathbf{r})\chi^\downarrow(s) \\
-                       &=& \, \phi^\uparrow(\mathbf{r}) e^{i s} + \phi^{\downarrow}(\mathbf{r}) e^{-i s}\:,
+    \phi(\mathbf{r},s) = \phi^\uparrow(\mathbf{r}) \chi^\uparrow(s) + \phi^{\downarrow}(\mathbf{r})\chi^\downarrow(s) \\
+                       =  \phi^\uparrow(\mathbf{r}) e^{i s} + \phi^{\downarrow}(\mathbf{r}) e^{-i s}
 
 where :math:`s` is the spin variable and using the complex spin representation.
 In order to carry out spin-orbit calculations in solids, the single-particle spinors
@@ -167,17 +167,17 @@ As described in :cite:`Melton2016-2`, the relativistic (semilocal) ECPs take the
 .. math::
   :label: seqn5
   
-  W^{\rm RECP} = W_{LJ}(r) + \sum_{\ell j m_j} W_{\ell j}(r) | \ell j m_j \rangle \langle \ell j m_j | \:,
+  W^{\rm RECP} = W_{LJ}(r) + \sum_{\ell j m_j} W_{\ell j}(r) | \ell j m_j \rangle \langle \ell j m_j |
 
 where the projectors :math:`|\ell j m_j\rangle` are the so-called spin spherical harmonics. 
 An equivalent formulation is to decouple the fully relativistic effective core potential (RECP) into *averaged relativistic* (ARECP)  and *spin-orbit* (SORECP) contributions:
 
 .. math::
   :label: seqn6
 
-  W^{\rm RECP} &=& \, W^{\rm ARECP} + W^{\rm SOECP} \\
-  W^{\rm ARECP} &=& \, W^{\rm ARECP}_L(r) + \sum_{\ell m_\ell} W_\ell^{ARECP}(r) | \ell m_\ell \rangle \langle \ell m_\ell| \\
-  W^{\rm SORECP} &=& \sum_\ell \frac{2}{2\ell + 1} \Delta W^{\rm SORECP}_\ell(r) \sum\limits_{m_\ell,m_\ell'} |\ell m_\ell\rangle \langle \ell m_\ell | \vec{\ell} \cdot \vec{s} | \ell m_\ell' \rangle \langle \ell m_\ell'|\:.
+  W^{\rm RECP} =  W^{\rm ARECP} + W^{\rm SOECP} \\
+  W^{\rm ARECP} =  W^{\rm ARECP}_L(r) + \sum_{\ell m_\ell} W_\ell^{ARECP}(r) | \ell m_\ell \rangle \langle \ell m_\ell| \\
+  W^{\rm SORECP} = \sum_\ell \frac{2}{2\ell + 1} \Delta W^{\rm SORECP}_\ell(r) \sum\limits_{m_\ell,m_\ell'} |\ell m_\ell \rangle \langle \ell m_\ell | \vec{\ell} \cdot \vec{s} | \ell m_\ell' \rangle \langle \ell m_\ell'|
 
 Note that the :math:`W^{\rm ARECP}` takes exactly the same form as 
 the semilocal pseudopotentials used in standard QMC calculations. 
@@ -188,8 +188,8 @@ We note the following relations between the two representations of the relativis
 .. math::
   :label: seqn7
 
-  W^{\rm ARECP}_\ell(r) &=& \frac{\ell+1}{2\ell+1} W^{\rm RECP}_{\ell,j=\ell+1/2}(r) + \frac{\ell}{2\ell+1} W^{\rm RECP}_{\ell,j=\ell-1/2}(r) \\
-  \Delta W^{\rm SORECP}_\ell(r) &=& W^{\rm RECP}_{\ell,j=\ell+1/2}(r) - W^{\rm RECP}_{\ell,j=\ell-1/2}(r)
+  W^{\rm ARECP}_\ell(r) = \frac{\ell+1}{2\ell+1} W^{\rm RECP}_{\ell,j=\ell+1/2}(r) + \frac{\ell}{2\ell+1} W^{\rm RECP}_{\ell,j=\ell-1/2}(r) \\
+  \Delta W^{\rm SORECP}_\ell(r) = W^{\rm RECP}_{\ell,j=\ell+1/2}(r) - W^{\rm RECP}_{\ell,j=\ell-1/2}(r)
 
 The structure of the spin-orbit ``.xml`` is