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+# Proposal for Periodic Boundary Conditions (PBC)
+
+## Problem
+Open Babel does not currently account for periodic boundary conditions.  Unit cells are isolated in space instead of accounting for bonds, distances, etc., to neighboring cells.
+
+This issue was migrated as [Github #1536](https://github.com/openbabel/openbabel/issues/1536) and is [requested](https://www.mail-archive.com/openbabel-discuss@lists.sourceforge.net/msg02002.html) [periodically](https://sourceforge.net/p/openbabel/mailman/message/7048390/) on the mailing list.
+
+> It would be great if OB could deal with structures and bond perception over periodic boundaries. This has already been implemented by G. Garberoglio in http://software-lisc.fbk.eu/obgmx/ but it would be great to get his patches merged into the standard version.
+
+
+## Proposed Enhancement
+
+Update the relevant methods in the API to apply the Minimum Image Convention for bond perception and geometric calculations, such as distances and angles.
+
+I briefly discussed this work with Giovanni Garberoglio, who shared his relevant source code with me.
+Our implementations were quite similar, so I am in the process of merging the best parts of our implementations together, which is currently in [my Open Babel repository](https://github.com/bbucior/openbabel/tree/periodic-boundaries).
+
+
+## Detailed Explanation
+
+### Theory
+One way to represent atoms/particles in a periodic cell is to wrap all of their fractional coordinates between 0 and 1.
+The minimum image convention is commonly used to calculate distances between two atoms in a unit cell.
+By way of example, when calculating an atom's neighbors (`OBMol::ConnectTheDots`), only the closest copy of the other atoms should be considered for the distance comparison.
+Otherwise, there would be infinite neighbors to consider.
+To apply these conditions, after subtracting the two positions, the fractional coordinates of the vector are standardized in the range (-0.5, 0.5), ensuring that two atoms are no farther than half a box length away (thus the nearest copy).
+
+### Implementation
+
+When a periodic molecule is read, an `OBMol::OB_PERIODIC_MOL` flag is set with the appropriate setters/getters.
+In my current implementation, the OBUnitCell is copied using methods like `OBMol::GetPeriodicLattice`.
+
+In order to actually apply periodic boundary conditions, the atoms and bonds need to be aware of them, so they refer back to the settings of the parent OBMol.
+Calls to vector-based calculations, such as `OBBond::GetLength`, automatically check for and apply periodicity conditions as necessary.
+During implementation, I found that many usages of geometric properties, such as bond lengths, calculate the properties ad-hoc using the atomic coordinates/vectors instead of using the standardized built-in methods, so I cleaned up these usages, particularly in the stereo code.
+
+The algorithm for the minimum image convention itself is now implemented as part of OBUnitCell, specifically in the functions `MinimumImageFractional(vector3)` and `MinimumImageCartesian(vector3)`.
+I also added helper functions `UnwrapCartesianNear` and `UnwrapFractionalNear` to unwrap coordinates (thus potentially a molecule) into absolute coordinates extending beyond the unit cell.
+For example, torsion is a four-body term.  Since the calculation extends beyond next-nearest neighbors, it is easiest to temporarily "unwrap" a copy of the relevant atoms so that they are in the same unit cell image.
+
+Enabling periodicity is now implemented as an input option for mmcif.
+An optional input flag is required to enable periodicity, which will help during the intermediate stages of implementation, when some use cases expect PBC (energy calculations) while others don't (png/svg formats).
+
+### Alternatives to consider
+1. **`OBMol::GetPeriodicLattice`, etc.:** The code could be simplified by removing these methods entirely and/or using the unit cell object already saved via `OBMol::SetData`.  If I refactor to that approach, accessing the lattice data would look something like `OBUnitCell * pCell = (OBUnitCell * )pmol->GetData(OBGenericDataType::UnitCell);`.
+2. **`OB_PERIODIC_MOL` flag:** The "periodic" property could be moved from a molecular flag to a bool setting within OBMol (like `_autoFormalCharge`)
+3. Can we avoid changing the `const` flag for `OBBond::GetLength()` without making a lot of other changes?
+4. Could consider saving the coordinates in a new, native OBCoord class instead of converting between Cartesian and fractional as much, but changes to the project may be considerably more involved.
+
+### Status
+Proof-of-concept code is written and has been tested as part of an ongoing research project.  Some changes are necessary before it's ready to merge upstream:
+
+1. Decide on the appropriate API and implementation details, then clean up the methods as necessary
+2. Write new formal test cases (what would be some good ideas?).  Verify that my changes do not break existing tests on the newest development version of Open Babel.
+3. Implement periodicity (or definitive STUB behavior) in areas like `OBBond::SetLength`, `OBBuilder`, and the SVG format.
+4. Update Open Babel version in periodic-boundaries branch to current and prepare PR
+
+### Edge cases
+
+1. Small unit cells
+
+Once periodic boundaries are applied, an atom could theoretically be bonded to its image (A-A') or twice to the same atom (A-B-A', which would use the A-B OBAtom pointers nonuniquely).
+The easiest method to address these cases would be issuing a warning if any of the lattice parameters are too small (defined as twice a reasonable maximum bond distance).
+Otherwise, OBBond and periodicity code would be far too complicated if it had to keep track of the atom images in other unit cells, and methods like `OBBond::GetBond(bgn, end)` will break and/or fail to capture every neighbor.
+
+2. Addition of molecules with dissimilar unit cells
+
+Should any additional checks be performed when two molecules are added together?
+Adding a nonperiodic OBMol to a periodic one?
+Adding two periodic structures together?
+There is a current ambiguity in the source code (`OBMol::operator+=`) for handling additions of 2D structures to 3D.
+Note that Materials Studio completely disallows adding periodic structures together unless their lattice parameters match.
+
+3. Atoms on the borders of unit cells
+
+Atoms near unit cell boundaries can easily cause errors if not handled consistently, for example in calculating relative positions between atoms in different unit cells.
+`OBUnitCell::WrapFractionalCoordinate` anticipates this using a fuzzy border, where atoms within a certain limit of the unit cell (1.0e-6 in fractional coordinates) are wrapped consistently.
+However, atoms may not necessarily be wrapped if read verbatim from a CIF or similar format.
+
+4. Are there any forseeable complications with symmetry operations?  I am not familiar with that code.
+
+
+## Pros and Cons
+
+Pros associated with this implementation include:
+
+* Minimal number of changes to lines of existing code
+* Hiding periodicity behind a flag can reduce compatibility issues
+* Once implemented, periodic bonds can be properly exported, e.g. CIF format or energy calculations
+* As a side benefit, this work will clean up code in the project to standardize how certain methods are used in the API.  For example, some files use `OBBond.GetLength()` while others manually recalculate the distance (or angle, torsion, etc.)
+
+Cons associated with this implementation include:
+
+* Certain formats become strange and nonstandard in periodic systems, e.g. SMILES of polymers are currently indistinguishable from a hydrocarbon ring
+* From limited testing, it appears that InChI cannot handle wrapped coordinates in the unit cell, particularly when determining stereochemistry
+* Possibility of breaking assumptions in downstream codes, though these projects are likely frozen on old versions of Open Babel
+* Updates to other formats, such as SVG, are required to make sure the output is still reasonable
+* Ease of introducing subtle bugs when handling periodic structures.  Maintenance could be more difficult depending on how contributors implement calculations (see also the last "pro" point above)
+* Not handling unit cells below a certain size
+
+
+## Interested Contributors
+@bbucior
+