/// <summary>
/// Enumerates over all orbital integrals with the same coefficient
/// as this.
/// These symmetries arise from:
/// - Indistinguishability of electrons.
/// - Orbitals are assumed to be real.
/// </summary>
/// <returns>Array of orbital integrals with the same coefficient.</returns>
public OrbitalIntegral[] EnumerateOrbitalSymmetries()
{
var coefficient = Coefficient;
if (OrbitalIndices.Length == 2)
{
var i = OrbitalIndices[0];
var j = OrbitalIndices[1];
var symmetries = new Int64[][]
{
new Int64[] { i, j },
new Int64[] { j, i }
};
return(symmetries.Distinct(new Extensions.IntArrayIEqualityComparer()).Select(o => new OrbitalIntegral(o, coefficient)).ToArray());
}
else if (OrbitalIndices.Length == 4)
{
var i = OrbitalIndices[0];
var j = OrbitalIndices[1];
var k = OrbitalIndices[2];
var l = OrbitalIndices[3];
var symmetries = new Int64[][] {
new Int64[] { i, j, k, l }, // 0123
new Int64[] { j, i, l, k }, // 1032
new Int64[] { k, l, i, j }, // 2301
new Int64[] { l, k, j, i }, // 3210
new Int64[] { i, k, j, l }, // 0213
new Int64[] { k, i, l, j }, // 2031
new Int64[] { j, l, i, k }, // 1302
new Int64[] { l, j, k, i } // 3120
};
return(symmetries.Distinct(new Extensions.IntArrayIEqualityComparer()).Select(o => new OrbitalIntegral(o, coefficient)).ToArray());
}
else
{
throw new System.NotImplementedException();
}
}