Description
Label a supplied angular-momentum shell and spherical degeneracy.
Molecular calculations use explicit energy, time, coordinate, spin and basis-function conventions. Spherical orbital degeneracy differs from Cartesian function count, an orbital-energy gap differs from an excitation energy, and a force-displacement energy term is local. Supplied occupations and reference values do not establish a converged electronic state or chemical interpretation.
Label a supplied angular-momentum shell and spherical degeneracy.
When to use this tool
Use Single Center Angular Momentum Label when you already have angularMomentum and need to label a supplied angular-momentum shell and spherical degeneracy.
How to use the tool and how it works
- Enter angularMomentum. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read shellLabel, degeneracy. Use the output convention below.
Require nonnegative safe angularMomentum; use s/p/d/f/g for 0..4 or l=N otherwise, and compute 2*l+1 with BigInt then safe numeric export.1
Spherical shells have 2l+1 spatial functions, while Cartesian shells have (l+1)(l+2)/2. The returned degeneracy uses the spherical convention and does not count spin or electrons.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| angularMomentum | Angular Momentum | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| shellLabel | Shell Label | Required. Text; maximum UTF-16 length 8192. |
| degeneracy | 2*l+1 spherical spatial functions, not Cartesian functions, spin multiplicity or electron count. | Required. Safe integer. |
{
"input": {
"angularMomentum": 2
},
"output": {
"shellLabel": "d",
"degeneracy": 5
}
}Limitations and assumptions
- Degeneracy counts spherical spatial functions, not Cartesian shell functions, spin states, electrons or primitives. Unsafe output counts are rejected.
- 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
Inspect the full computational method, basis, geometry, reference state and convergence records. Use a complete electronic-structure or dynamics calculation for physical conclusions; local sign, unit and index transformations do not perform that calculation.
References
Similar or alternative tools
- Quantum Chemistry Basis Primitive Count
Sum supplied shell primitive counts with exact integer intermediates.
- Electronic Structure Spin Contamination Gap
Compare supplied spin-squared expectation with a target-spin reference.