Qn Network Analysis

Purpose

To create FNC or Topology input for RMC_POT, it is necessary to determine which atoms form each local structure. This library represents a local structure using three layers:

Central
      │
   Bridge
      │
Second

For SiO₂, this corresponds to:

Si
 │
 O
 │
Si

The library analyzes this network to obtain Qn values and bond information.

Network Model

The general network representation is:

Central ----- Bridge ----- Second

Atomic species are specified in JSON. For SiO₂:

Central : Si
Bridge  : O
Second  : Si

This design makes the analysis algorithm itself independent of SiO₂.

Definition of Qn

Qn is defined as the number of Bridge atoms bonded to a Central atom that are also bonded to another Central atom. For example:

      Si
      │
O─────┼─────O
│           │
Si         Si

This corresponds to Q2. A Bridge atom that is not connected to another Central atom is treated as a non-bridging oxygen (NBO) in the SiO₂ case.

Analysis Procedure

The analysis proceeds approximately as follows:

POSCAR
  ↓
Extract atomic species
  ↓
Select Central atoms
  ↓
Select Bridge atoms
  ↓
Select Second atoms
  ↓
Search Central–Bridge neighbors
  ↓
Search Bridge–Second neighbors
  ↓
Identify bridging atoms
  ↓
Determine Qn
  ↓
Generate bond information
  ↓
Generate angle information
  ↓
Generate FNC pairs

1. Extracting Atomic Species

Atomic species are read from POSCAR and classified according to the JSON entries central_types, bridge_types, and second_types. No distance-based selection is performed at this stage.

2. Central–Bridge Search

Neighbors between Central and Bridge atoms are identified using one of two methods: cutoff or nearest.

cutoff

All atoms whose distances lie between first_min and first_max are selected.

nearest

Only the specified number N of candidates satisfying the distance conditions are selected. For SiO₂, nearest = 4 is commonly used to obtain SiO₄ tetrahedra consistently.

3. Bridge–Second Search

Second atoms are identified from the perspective of each Bridge atom. Two methods are available.

second_use_first_network = false

A new distance-based search is performed around each Bridge atom to find Second atoms, for example O → Si. This is the simplest method.

second_use_first_network = true

No separate Bridge–Second search is performed. Instead, the previously determined Central → Bridge network is reversed to construct Bridge → Second connections.

This approach preserves consistency between the Central–Bridge and Bridge–Second relationships and is recommended for SiO₂.

4. Identifying Bridging Atoms

For each Bridge atom, the number of connected Second atoms is examined. The original Central atom is excluded; only connections to another Central atom qualify the atom as a bridge.

5. Determining Qn

For each Central atom, the number of Bridge atoms connected to another Central atom is counted:

shared bridges → Q4
shared bridges → Q3
shared bridges → Q2

Qn does not count all Bridge neighbors. It counts only those shared with another Central atom.

Analysis Results

The analysis generates:

Qn values for each Central atom.
Bridge information.
Bond information.
Angle information.
FNC pairs.

These are abstract network data independent of RMC formatting. The subsequent writer uses only these results to generate RMC_POT FNC and Topology files:

Analysis
   ↓
Abstract network
   ↓
RMC files

This three-stage design keeps the analysis algorithm and output format independent.