Atomic Center Coordinate Reference Tool

Description

Return relative three-dimensional coordinates and their norm.

Computational chemistry separates composition and electron bookkeeping from basis conventions, coordinates, quadrature and energetic weights. A local exact count or unit conversion can be consistent without identifying a valid electronic state, optimized structure or normalized thermodynamic ensemble.

Return relative three-dimensional coordinates and their norm.

When to use this tool

Use Atomic Center Coordinate Reference when checking a supplied computational-chemistry count, coordinate, basis or weighting convention.

How to use the tool and how it works

Enter coordinate, referenceCenter, unitToCommon. Keep parallel arrays aligned. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read relativeCoordinate, distance. Use the output convention below.

Return relative three-dimensional coordinates and their norm. Require exactly three coordinate/referenceCenter entries and unitToCommon > 0; subtract corresponding center components, multiply by unit factor and use hypot.^[1]

Input field	Meaning and units	Accepted input
coordinate	Coordinate	Required. Array of finite number; maximum items 256.
referenceCenter	Reference Center	Required. Array of finite number; maximum items 256.
unitToCommon	Unit To Common	Required. Finite number; strictly above 0.

Output field	Interpretation	Returned shape
relativeCoordinate	Relative Coordinate	Required. Array of finite number; maximum items 256.
distance	Distance	Required. Finite number.

json

{
  "input": {
    "coordinate": [
      4,
      6,
      3
    ],
    "referenceCenter": [
      1,
      2,
      3
    ],
    "unitToCommon": 2
  },
  "output": {
    "relativeCoordinate": [
      6,
      8,
      0
    ],
    "distance": 10
  }
}

Limitations and assumptions

Coordinates and center must initially share units; periodic images, atomic identity and molecular alignment are not inferred.
Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Use a complete verified electronic-structure or statistical-mechanical model and compatible property/unit conventions for actual molecular inference.

References

Calculation and input contract: computational-chemistry/atomic-center-coordinate-reference — tool.io

Similar or alternative tools

Atomic Force Zero Reference Gap
Return reference-corrected force and a symmetric envelope.
Atomic Coordinate Unit Label
Label one supplied 3D atomic coordinate with its declared unit without performing coordinate or unit conversion.