deploy: 1b94274

.buildinfo

@@ -1,4 +1,4 @@
 # Sphinx build info version 1
 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
-config: b1197c47ffd48e04f500c588515f3ac8
+config: cf210c7a0acbca206f137f9bcc007006
 tags: 645f666f9bcd5a90fca523b33c5a78b7

_sources/background/algorithms/cap_methods/fmo.rst.txt

@@ -1,3 +1,17 @@
+.. Copyright 2024 GhostFragment
+..
+.. Licensed under the Apache License, Version 2.0 (the "License");
+.. you may not use this file except in compliance with the License.
+.. You may obtain a copy of the License at
+..
+.. http://www.apache.org/licenses/LICENSE-2.0
+..
+.. Unless required by applicable law or agreed to in writing, software
+.. distributed under the License is distributed on an "AS IS" BASIS,
+.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+.. See the License for the specific language governing permissions and
+.. limitations under the License.
+
 ##################
 FMO Capping Method
 ##################

_sources/background/algorithms/cap_methods/h_capping.rst.txt

@@ -1,3 +1,17 @@
+.. Copyright 2024 GhostFragment
+..
+.. Licensed under the Apache License, Version 2.0 (the "License");
+.. you may not use this file except in compliance with the License.
+.. You may obtain a copy of the License at
+..
+.. http://www.apache.org/licenses/LICENSE-2.0
+..
+.. Unless required by applicable law or agreed to in writing, software
+.. distributed under the License is distributed on an "AS IS" BASIS,
+.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+.. See the License for the specific language governing permissions and
+.. limitations under the License.
+
 #########
 H Capping
 #########

_sources/background/algorithms/cap_methods/index.rst.txt

@@ -1,3 +1,17 @@
+.. Copyright 2024 GhostFragment
+..
+.. Licensed under the Apache License, Version 2.0 (the "License");
+.. you may not use this file except in compliance with the License.
+.. You may obtain a copy of the License at
+..
+.. http://www.apache.org/licenses/LICENSE-2.0
+..
+.. Unless required by applicable law or agreed to in writing, software
+.. distributed under the License is distributed on an "AS IS" BASIS,
+.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+.. See the License for the specific language governing permissions and
+.. limitations under the License.
+
 ###############
 Capping Methods
 ###############

_sources/background/algorithms/cap_methods/other_caps.rst.txt

@@ -1,3 +1,17 @@
+.. Copyright 2024 GhostFragment
+..
+.. Licensed under the Apache License, Version 2.0 (the "License");
+.. you may not use this file except in compliance with the License.
+.. You may obtain a copy of the License at
+..
+.. http://www.apache.org/licenses/LICENSE-2.0
+..
+.. Unless required by applicable law or agreed to in writing, software
+.. distributed under the License is distributed on an "AS IS" BASIS,
+.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+.. See the License for the specific language governing permissions and
+.. limitations under the License.
+
 ###################
 Other Types of Caps
 ###################

_sources/background/algorithms/embed_methods/density.rst.txt

@@ -1,3 +1,17 @@
+.. Copyright 2024 GhostFragment
+..
+.. Licensed under the Apache License, Version 2.0 (the "License");
+.. you may not use this file except in compliance with the License.
+.. You may obtain a copy of the License at
+..
+.. http://www.apache.org/licenses/LICENSE-2.0
+..
+.. Unless required by applicable law or agreed to in writing, software
+.. distributed under the License is distributed on an "AS IS" BASIS,
+.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+.. See the License for the specific language governing permissions and
+.. limitations under the License.
+
 .. _density_embedding:
 
 #################

_sources/background/algorithms/embed_methods/index.rst.txt

@@ -1,3 +1,17 @@
+.. Copyright 2024 GhostFragment
+..
+.. Licensed under the Apache License, Version 2.0 (the "License");
+.. you may not use this file except in compliance with the License.
+.. You may obtain a copy of the License at
+..
+.. http://www.apache.org/licenses/LICENSE-2.0
+..
+.. Unless required by applicable law or agreed to in writing, software
+.. distributed under the License is distributed on an "AS IS" BASIS,
+.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+.. See the License for the specific language governing permissions and
+.. limitations under the License.
+
 ####################
 Embedding Algorithms
 ####################

_sources/background/algorithms/embed_methods/point_charge.rst.txt

@@ -1,3 +1,17 @@
+.. Copyright 2024 GhostFragment
+..
+.. Licensed under the Apache License, Version 2.0 (the "License");
+.. you may not use this file except in compliance with the License.
+.. You may obtain a copy of the License at
+..
+.. http://www.apache.org/licenses/LICENSE-2.0
+..
+.. Unless required by applicable law or agreed to in writing, software
+.. distributed under the License is distributed on an "AS IS" BASIS,
+.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+.. See the License for the specific language governing permissions and
+.. limitations under the License.
+
 ######################
 Point Charge Embedding
 ######################
@@ -62,7 +76,7 @@ means one:
 #. Recompute the point charges for each fragment. This time instead of 
    neglecting atoms outside the fragment, replace them with their computed point
    charge.
-#. Repeat the previous step until convergence.
+#. Repeat the previous step until convergence or for a set number of iterations
 
 Variations
 ==========

_sources/background/algorithms/frag_methods/dclc.rst.txt

@@ -1,3 +1,17 @@
+.. Copyright 2024 GhostFragment
+..
+.. Licensed under the Apache License, Version 2.0 (the "License");
+.. you may not use this file except in compliance with the License.
+.. You may obtain a copy of the License at
+..
+.. http://www.apache.org/licenses/LICENSE-2.0
+..
+.. Unless required by applicable law or agreed to in writing, software
+.. distributed under the License is distributed on an "AS IS" BASIS,
+.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+.. See the License for the specific language governing permissions and
+.. limitations under the License.
+
 .. _DCLC_fragmentation_method:
 
 #########################################################

_sources/background/algorithms/frag_methods/fea.rst.txt

@@ -1,3 +1,17 @@
+.. Copyright 2024 GhostFragment
+..
+.. Licensed under the Apache License, Version 2.0 (the "License");
+.. you may not use this file except in compliance with the License.
+.. You may obtain a copy of the License at
+..
+.. http://www.apache.org/licenses/LICENSE-2.0
+..
+.. Unless required by applicable law or agreed to in writing, software
+.. distributed under the License is distributed on an "AS IS" BASIS,
+.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+.. See the License for the specific language governing permissions and
+.. limitations under the License.
+
 
 .. _fea_frag_method:
 

_sources/background/algorithms/frag_methods/gebf.rst.txt

@@ -1,10 +1,25 @@
+.. Copyright 2024 GhostFragment
+..
+.. Licensed under the Apache License, Version 2.0 (the "License");
+.. you may not use this file except in compliance with the License.
+.. You may obtain a copy of the License at
+..
+.. http://www.apache.org/licenses/LICENSE-2.0
+..
+.. Unless required by applicable law or agreed to in writing, software
+.. distributed under the License is distributed on an "AS IS" BASIS,
+.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+.. See the License for the specific language governing permissions and
+.. limitations under the License.
+
 ##########################
 GEBF Fragmentation Methods
 ##########################
 
 .. |zeta| replace:: :math:`\zeta`
-.. |g| replace:: :math:`g`
-.. |Fg| replace:: :math:`F_g`
+.. |i| replace:: :math:`i`
+.. |eta| replace:: :math:`\eta`
+.. |etam1| replace:: :math:`\left(\eta -1\right)`
 
 .. _gebf07_fragmentation_method:
 
@@ -42,4 +57,123 @@ presented namely:
 - Look for a set of :math:`n-1` pseudoatoms which appears in more than one
   fragment. The multiplicity of this intersection is :math:`1-k`, where :math`k`
   is the number of fragments it appears in.
-- Repeat the previous step for sets of :math`n-2, n-3, \ldots, 1` pseudoatoms 
+- Repeat the previous step for sets of :math`n-2, n-3, \ldots, 1` pseudoatoms 
+
+.. _gebf08_fragmentation_method:
+
+***************************
+GEBF08 Fragmentation Method
+***************************
+
+:cite:t:`Hua_2008` introduced a new fragmentation method for the GEBF method:
+
+1. Define |eta|, the maximum number of pseudoatoms in a fragment.
+2. Form pseudoatoms.
+3. For each pseudoatom combine it with the |etam1| closest pseudoatoms to form
+   a fragment.
+
+.. _gebf10_fragmentation_method:
+
+***************************
+GEBF10 Fragmentation Method
+***************************
+
+.. |Pi| replace:: :math:`P_i`
+.. |Pj| replace:: :math:`P_j`
+.. |Fi| replace:: :math:`F_i`
+.. |Fj| replace:: :math:`F_j`
+
+:cite:t:`Hua2010` introduced a new fragmention method for the GEBF method. The
+first steps are just the GEBF07 method (minus the distinction between molecular
+clusters and covalent systems):
+
+#. Define a distance threshold |zeta|
+#. Determine pseudoatoms, the |i|-th pseudoatom is denoted |Pi|
+#. The |i|-th fragment, |Fi|, include |Pi| and all pseudoatoms within |zeta| of
+   it.
+
+The remainder of the algorithm amounts to "extension rules" which extend the
+fragments:
+
+4. For each fragment check for incomplete rings. If the fragment contains an
+   incomplete ring, complete it by adding the pseudoatoms spanning the rest
+   of the ring. If the resulting structure still has incomplete rings repeat
+   this step one more time. Do not repeat the step beyond the second time.
+#. For each fragment consider pseudoatoms with dangling bonds. Say |Pi| has 
+   dangling bonds, then if |Pi| contains three or more heavy atoms, or if |Pi| 
+   was added by the previous step ignore it. If |Pi| was not ignored then add to
+   the fragment each pseudoatom bonded to |Pi|. If |Pi| contains only 1 heavy 
+   atom then for each pseudoatom bonded to |Pi|, |Pj|, additionaly add the
+   pseudoatoms bonded to |Pj|.
+
+At this point caps are added (:cite:t:`Hua2010` use 
+:ref:`standard_distance_capping`).
+
+.. _gebf12_fragmentation_method:
+
+***************************
+GEBF12 Fragmentation Method
+***************************
+
+:cite:t:`Hua2012` built on the GEBF10 Fragmentation method to create the GEBF12
+fragmentation method.
+
+#. Create fragments subject to the :ref:`gebf10_fragmentation_method`.
+#. Find the pairs of pseudoatoms, |Pi| and |Pj|, separated by a distance less
+   than :math:`2\zeta`.
+#. For each pair from step 2, determine if a pair from step 1 contains the
+   pair, if not create a new fragment which contains the |Pi| and |Pj| and
+   all other pseudoatoms which are within |zeta| of the geometric center of
+   |Pi| and |Pj|.
+#. Apply extension rules (see :ref:`gebf10_fragmentation_method`) to each 
+   fragment formed in step 3. 
+
+.. _gebf14_fragmenation_method:
+
+***************************
+GEBF14 Fragmentation Method
+***************************
+
+:cite:t:`Wang2014` combined the GEBF08 and GEBF12 fragmenation methods to create
+the GEBF14 method. In their presentation, :cite:t:`Wang2014` did not discuss the
+extension rules; however, because the application was water clusters, the
+extension rules were not relevant. For clarity the GEBF14 procedure is:
+
+#. Define a distance threshold |zeta|
+#. Define a maximum number of pseudoatoms |eta|.
+#. Determine pseudoatoms, the |i|-th pseudoatom is denoted |Pi|
+#. The |i|-th fragment, |Fi|, include |Pi| and all pseudoatoms within |zeta| of
+   it. If more than |eta| pseudoatoms fall within a radius of |zeta| only the
+   |eta| closest to |Pi| are included.
+#. Presumably extension rules are applied here.
+#. Find the pairs of pseudoatoms, |Pi| and |Pj|, separated by a distance less
+   than :math:`2\zeta`.
+#. For each pair from step 2, determine if a pair from step 1 contains the
+   pair, if not create a new fragment which contains the |Pi| and |Pj| and
+   all other pseudoatoms which are within |zeta| of the geometric center of
+   |Pi| and |Pj|. If more than |eta| pseudoatoms fall within a radius of |zeta| 
+   only the |eta| closest to the geometric center of |Pi| and |Pj| are included.
+#. Apply extension rules (see :ref:`gebf10_fragmentation_method`) to each 
+   fragment formed in step 3. 
+
+.. _gebf19_fragmentation_method:
+
+***************************
+GEBF19 Fragmentation Method
+***************************
+
+:cite:t:`Li_2019` proposed a new fragmentation method designed to produce
+smaller fragments then GEBF14 when applied to host/guest complexes.
+
+#. Define a distance threshold |zeta|
+#. Define a mximum number of pseudoatoms |eta|.
+#. Determine pseudoatoms, the |i|-th pseudoatom is denoted |Pi|.
+#. For |Pi| form a fragment, |Fi|, which contains |Pi| and all pseudoatoms that
+   are within |zeta| of |Pi|. |Pi| is considered colored in |Fi|.
+#. For each fragment |Fi| with more pseudoatoms than |eta|, create new fragments
+   for each un-colored pseudoatom |Pj| in |Fi|. The fragment resulting from
+   |Pj| is |Fj| and includes |Pj|, the colored pseudoatoms, and the un-colored
+   pseudoatoms in |Fi| which are within |zeta| of |Pj|. |Pj| is considered c
+   olored in |Fj|. Discard |Fi|.
+#. Repeat the previous step until no fragments contain more pseudoatoms than
+   |eta| or all pseudoatoms have been colored.

_sources/background/algorithms/frag_methods/index.rst.txt

@@ -1,3 +1,17 @@
+.. Copyright 2024 GhostFragment
+..
+.. Licensed under the Apache License, Version 2.0 (the "License");
+.. you may not use this file except in compliance with the License.
+.. You may obtain a copy of the License at
+..
+.. http://www.apache.org/licenses/LICENSE-2.0
+..
+.. Unless required by applicable law or agreed to in writing, software
+.. distributed under the License is distributed on an "AS IS" BASIS,
+.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+.. See the License for the specific language governing permissions and
+.. limitations under the License.
+
 ########################
 Fragmentation Algorithms
 ########################

_sources/background/algorithms/frag_methods/mfcc.rst.txt

@@ -1,3 +1,17 @@
+.. Copyright 2024 GhostFragment
+..
+.. Licensed under the Apache License, Version 2.0 (the "License");
+.. you may not use this file except in compliance with the License.
+.. You may obtain a copy of the License at
+..
+.. http://www.apache.org/licenses/LICENSE-2.0
+..
+.. Unless required by applicable law or agreed to in writing, software
+.. distributed under the License is distributed on an "AS IS" BASIS,
+.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+.. See the License for the specific language governing permissions and
+.. limitations under the License.
+
 .. _mfcc_frag_method:
 
 #########################

_sources/background/algorithms/frag_methods/mta.rst.txt

@@ -1,3 +1,17 @@
+.. Copyright 2024 GhostFragment
+..
+.. Licensed under the Apache License, Version 2.0 (the "License");
+.. you may not use this file except in compliance with the License.
+.. You may obtain a copy of the License at
+..
+.. http://www.apache.org/licenses/LICENSE-2.0
+..
+.. Unless required by applicable law or agreed to in writing, software
+.. distributed under the License is distributed on an "AS IS" BASIS,
+.. WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+.. See the License for the specific language governing permissions and
+.. limitations under the License.
+
 ##########################################
 Molecular Tailoring Approach Fragmentation
 ##########################################