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Electronic Structure Spin Contamination Gap

Subtract target S(S+1) from a supplied expectation of spin squared expressed in hbar-squared units for an explicit integer or half-integer spin.

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Description

Compare supplied spin-squared expectation with a target-spin reference.

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.

Compare supplied spin-squared expectation with a target-spin reference.

When to use this tool

Use Electronic Structure Spin Contamination Gap when you already have computedS2, targetSpin and need to compare supplied spin-squared expectation with a target-spin reference.

How to use the tool and how it works

  1. Enter computedS2, targetSpin. Use the units and conventions below.
  2. Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
  3. Read targetS2, contamination. Use the output convention below.

Require computedS2>=0 and targetSpin a nonnegative integer or half-integer; targetS2=S*(S+1), contamination=computedS2-targetS2.1

Input fieldMeaning and unitsAccepted input
computedS2Computed S2 Unit: ħ².Required. Finite number; minimum 0.
targetSpinNonnegative S with 2*S integral; spin quantum number rather than multiplicity.Required. Finite number; minimum 0.
Output fieldInterpretationReturned shape
targetS2Target S2 Unit: ħ².Required. Finite number.
contaminationcomputedS2-S*(S+1), retaining negative differences; no adequacy threshold is chosen. Unit: ħ².Required. Finite number.
json
{
  "input": {
    "computedS2": 1,
    "targetSpin": 0.5
  },
  "output": {
    "targetS2": 0.75,
    "contamination": 0.25
  }
}

Limitations and assumptions

  • The usual dimensionless hbar-squared convention is assumed. Negative differences are accepted; no wavefunction, target multiplicity, acceptable contamination or physical spin state is validated.
  • 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

  1. Calculation and input contract: computational-chemistry/electronic-structure-spin-contamination-gap — tool.io

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