Terminology Used Throughout GhostFragment

There are a lot of existing fragment-based methods. Many of these methods have coined their own terms for similar concepts. In order to provide a unified description of these methods we have settled on the following terminology.

capping

When fragmenting one usually tries to split the system across non-covalent interactions; however, if one is to divide a large covalently bonded system into fragments it becomes necessary to “break” covalent bonds (a covalent bond is said to be broken when only one of the atoms involved in the bond appear in a fragment). When a fragment contains a broken bond, running the computation as is will usually result in an unphysical electronic state (the fragment will have a different spin state than the overall system). Capping methods ensure the fragment has the same spin state as the parent system (usually by adding a hydrogen atom).

dimer(s)

A subsystem made by taking the union of two monomers

fragment(x)

The inputs to the MBE and GMBE. Fragments are sets of pseudoatoms.

monomer(s)

Same as fragment, but preferred when subsystems are being distinguished by numerical prefix. i.e., we use monomer, and not fragment, when we are also talking about dimers, trimers, etc.

multi-layer

Refers to when the final fragment-based method is put together in an ONIOM- like manner. The layers can be different theories, different fragmentations, etc.

n-mer(s)

The generalization of monomer, dimer, etc. to the union of :math`n` fragments.

pseudoatom(s)

In fragmenting the supersystem there are some “most fundamental” units, i.e. units which themselves are never fragmented. In the most extreme limit these fundamental units are the individual atoms; however, in most fragmentation algorithms the fundamental units involve several atoms. For example, in fragmenting a molecular cluster a popular and obvious choice is to take the molecules as the fundamental units. Regardless of their composition, the most fundamental units of the fragmentation algorithm are termed “pseudoatoms.”

supersystem

This is the system whose properties are actually of interest. Its properties are computed by fragmenting it into subsystems.

Graph Theory Terminology

Particularly when describing fragmentation algorithms we often treat the supersystem as a mathematical graph.

edge

These are the connections between two nodes in the graph. They will usually correspond to covalent bonds, but exactly what defines an edge is usually left up to the user.

degree

This is the number of edges a node has.

leaf

This is a node with degree 1.

node

In the context of a molecular graph nodes are typically pseudoatoms.