Description
Return functions in one angular-momentum shell.
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 functions in one angular-momentum shell.
When to use this tool
Use Computational Chemistry: Basis Shell Cartesian Spherical Count when checking a supplied computational-chemistry count, coordinate, basis or weighting convention.
How to use the tool and how it works
- Enter angularMomentum, convention. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Return functions in one angular-momentum shell. Require angularMomentum l in [0,32] and convention cartesian or spherical; count is (l+1)*(l+2)/2 or 2*l+1 respectively.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| angularMomentum | Angular Momentum | Required. Safe integer. |
| convention | Convention | Required. Text; one of "cartesian", "spherical". Implementation limit: 8192 Unicode code points and 16384 UTF-16 code units. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Returned calculated value or nested object under the stated output convention. | Required. Object. |
| result.functionCount | Function Count | Calculated result member: number. |
{
"input": {
"angularMomentum": 2,
"convention": "cartesian"
},
"output": {
"result": {
"functionCount": 6
}
}
}Limitations and assumptions
- This counts one shell's angular components; contractions, primitives and actual basis-library definitions are not included.
- Outputs are nested inside result. 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
Similar or alternative tools
- Basis Function Count Contribution
Return gross and retained basis-function totals.
- Basis Exponent Length Unit Factor
Convert a Gaussian exponent under a length-unit change.