/// <summary>
/// Updates an instance of <see cref="FermionHamiltonian"/>
/// with all spin-orbitals from described by a sequence of two-body orbital integrals.
/// </summary>
/// <param name="nOrbitals">Total number of distinct orbitals.</param>
/// <param name="hpqTerms">Sequence of two-body orbital integrals.</param>
/// <param name="hamiltonian">Fermion Hamiltonian to be updated.</param>
public void CreateTwoBodySpinOrbitalTerms(OrbitalIntegral orbitalIntegral)
{
// One-electron orbital integral symmetries
// ij = ji
var pqSpinOrbitals = orbitalIntegral.EnumerateOrbitalSymmetries().EnumerateSpinOrbitals();
var coefficient = orbitalIntegral.Coefficient;
foreach (var pq in pqSpinOrbitals)
{
var p = pq[0];
var q = pq[1];
var pInt = p.ToInt();
var qInt = q.ToInt();
if (pInt == qInt)
{
AddFermionTerm(FermionTermType.Common.PPTermType, new FermionTerm {
CreationAnnihilationIndices = new Int64[] { 1, 0 }, SpinOrbitalIndices = pq, coeff = coefficient
});
}
else if (pInt < qInt)
{
AddFermionTerm(FermionTermType.Common.PQTermType, new FermionTerm {
CreationAnnihilationIndices = new Int64[] { 1, 0 }, SpinOrbitalIndices = pq, coeff = 2.0 * coefficient
});
}
}
}
/// <summary>
/// Method for adding to a <see cref="FermionHamiltonian"/>.
/// all <see cref="FermionTerm"/> generalted by all all symmetries of
/// <see cref="OrbitalIntegral.EnumerateOrbitalSymmetries"/> and
/// <see cref="OrbitalIntegral.EnumerateSpinOrbitals"/>.
/// </summary>
/// <param name="termType"><see cref="OrbitalIntegral"/> representing terms to be added.</param>
public void AddFermionTerm(OrbitalIntegral orbitalIntgral)
{
if (orbitalIntgral.Length() == 2)
{
CreateTwoBodySpinOrbitalTerms(orbitalIntgral);
}
else if (orbitalIntgral.Length() == 4)
{
CreateFourBodySpinOrbitalTerms(orbitalIntgral);
}
else
{
throw new System.NotImplementedException();
}
}
/// <summary>
/// Updates an instance of <see cref="FermionHamiltonian"/>
/// with all spin-orbitals from described by a sequence of four-body orbital integrals.
/// </summary>
/// <param name="nOrbitals">Total number of distinct orbitals.</param>
/// <param name="rawPQRSTerms">Sequence of four-body orbital integrals.</param>
/// <param name="hamiltonian">Fermion Hamiltonian to be updated.</param>
public void CreateFourBodySpinOrbitalTerms(OrbitalIntegral orbitalIntegral)
{
// Two-electron orbital integral symmetries
// ijkl = lkji = jilk = klij = ikjl = ljki = kilj = jlik.
var pqrsSpinOrbitals = orbitalIntegral.EnumerateOrbitalSymmetries().EnumerateSpinOrbitals();
var coefficient = orbitalIntegral.Coefficient;
// We only need to see one of these.
// Now iterate over pqrsArray
foreach (var pqrs in pqrsSpinOrbitals)
{
var p = pqrs[0];
var q = pqrs[1];
var r = pqrs[2];
var s = pqrs[3];
var pInt = p.ToInt();
var qInt = q.ToInt();
var rInt = r.ToInt();
var sInt = s.ToInt();
// Only consider terms on the lower diagonal due to Hermitian symmetry.
// For terms with two different orbital indices, possibilities are
// PPQQ (QQ = 0), PQPQ, QPPQ (p<q), PQQP, QPQP (p<q), QQPP (PP=0)
// Hence, if we only count PQQP, and PQPQ, we need to double the coefficient.
// iU jU jU iU | iU jD jD iD | iD jU jU iD | iD jD jD iD
if (pInt == sInt && qInt == rInt && pInt < qInt)
{ // PQQP
AddFermionTerm(FermionTermType.Common.PQQPTermType, new FermionTerm {
CreationAnnihilationIndices = new Int64[] { 1, 1, 0, 0 }, SpinOrbitalIndices = new SpinOrbital[] { p, q, r, s }, coeff = 1.0 * coefficient
});
}
else if (pInt == rInt && qInt == sInt && pInt < qInt)
{
// iU jU iU jU | iD jD iD jD
// PQPQ
AddFermionTerm(FermionTermType.Common.PQQPTermType, new FermionTerm {
CreationAnnihilationIndices = new Int64[] { 1, 1, 0, 0 }, SpinOrbitalIndices = new SpinOrbital[] { p, q, s, r }, coeff = -1.0 * coefficient
});
}
else if (qInt == rInt && pInt < sInt && rInt != sInt && pInt != qInt)
{
// PQQR
// For any distinct pqr, [i;j;j;k] generates PQQR ~ RQQP ~ QPRQ ~ QRPQ. We only need to record one.
if (rInt < sInt)
{
if (pInt < qInt)
{
AddFermionTerm(FermionTermType.Common.PQQRTermType, new FermionTerm {
CreationAnnihilationIndices = new Int64[] { 1, 1, 0, 0 }, SpinOrbitalIndices = new SpinOrbital[] { p, q, s, r }, coeff = -2.0 * coefficient
});
}
else
{
AddFermionTerm(FermionTermType.Common.PQQRTermType, new FermionTerm {
CreationAnnihilationIndices = new Int64[] { 1, 1, 0, 0 }, SpinOrbitalIndices = new SpinOrbital[] { q, p, s, r }, coeff = 2.0 * coefficient
});
}
}
else
{
if (pInt < qInt)
{
AddFermionTerm(FermionTermType.Common.PQQRTermType, new FermionTerm {
CreationAnnihilationIndices = new Int64[] { 1, 1, 0, 0 }, SpinOrbitalIndices = new SpinOrbital[] { p, q, r, s }, coeff = 2.0 * coefficient
});
}
else
{
AddFermionTerm(FermionTermType.Common.PQQRTermType, new FermionTerm {
CreationAnnihilationIndices = new Int64[] { 1, 1, 0, 0 }, SpinOrbitalIndices = new SpinOrbital[] { q, p, r, s }, coeff = -2.0 * coefficient
});
}
}
}
else if (qInt == sInt && pInt < rInt && rInt != sInt && pInt != sInt)
{
// PQRQ
// For any distinct pqr, [i;j;k;j] generates {p, q, r, q}, {q, r, q, p}, {q, p, q, r}, {r, q, p, q}. We only need to record one.
if (pInt < qInt)
{
if (rInt > qInt)
{
AddFermionTerm(FermionTermType.Common.PQQRTermType, new FermionTerm {
CreationAnnihilationIndices = new Int64[] { 1, 1, 0, 0 }, SpinOrbitalIndices = new SpinOrbital[] { p, q, r, s }, coeff = 2.0 * coefficient
});
}
else
{
AddFermionTerm(FermionTermType.Common.PQQRTermType, new FermionTerm {
CreationAnnihilationIndices = new Int64[] { 1, 1, 0, 0 }, SpinOrbitalIndices = new SpinOrbital[] { p, q, s, r }, coeff = -2.0 * coefficient
});
}
}
else
{
AddFermionTerm(FermionTermType.Common.PQQRTermType, new FermionTerm {
CreationAnnihilationIndices = new Int64[] { 1, 1, 0, 0 }, SpinOrbitalIndices = new SpinOrbital[] { q, p, r, s }, coeff = -2.0 * coefficient
});
}
}
else if (pInt < qInt && pInt < rInt && pInt < sInt && qInt != rInt && qInt != sInt && rInt != sInt)
{
// PQRS
// For any distinct pqrs, [i;j;k;l] generates
// {{p, q, r, s}<->{s, r, q, p}<->{q, p, s, r}<->{r, s, p, q},
// {1,2,3,4}<->{4,3,2,1}<->{2,1,4,3}<->{3,4,1,2}
// {p, r, q, s}<->{s, q, r, p}<->{r, p, s, q}<->{q, s, p, r}}
// 1324, 4231, 3142, 2413
if (rInt < sInt)
{
AddFermionTerm(FermionTermType.Common.PQRSTermType, new FermionTerm {
CreationAnnihilationIndices = new Int64[] { 1, 1, 0, 0 }, SpinOrbitalIndices = new SpinOrbital[] { p, q, s, r }, coeff = -2.0 * coefficient
});
}
else
{
AddFermionTerm(FermionTermType.Common.PQRSTermType, new FermionTerm {
CreationAnnihilationIndices = new Int64[] { 1, 1, 0, 0 }, SpinOrbitalIndices = new SpinOrbital[] { p, q, r, s }, coeff = 2.0 * coefficient
});
}
}
}
}
/// <summary>
/// Loads a Hamiltonian from integral data represented
/// in LIQ𝑈𝑖|⟩ format.
/// Please see the <a href="https://stationq.github.io/Liquid/docs/LIQUiD.pdf">
/// LIQ𝑈𝑖|⟩ documentation</a> for further details about the
/// format parsed by this method.
/// </summary>
/// <param name="lines">Sequence of text describing terms of Hamiltonian.</param>
/// <returns>
/// An instance of <see cref="FermionHamiltonian"/> representing the
/// data contained in <paramref name="lines"/>.
/// </returns>
public static FermionHamiltonian LoadFromLiquid(string line)
{
var regexMiscellaneous = new Regex(@"((info=(?<info>[^\s]*)))");
var regexnuc = new Regex(@"nuc=(?<nuc>-?\s*\d*.\d*)");
var regexPQ = new Regex(@"(^|\s+)(?<p>\d+),(?<q>\d+)\D*=\s*(?<coeff>-?\s*\d*.\d*)e?(?<exponent>-?\d*)");
var regexPQRS = new Regex(@"(^|\s+)(?<p>\d+)\D+(?<q>\d+)\D+(?<r>\d+)\D+(?<s>\d+)\D*=\s*(?<coeff>-?\s*\d*.\d*)e?(?<exponent>-?\d*)");
Double coulombRepulsion = 0.0;
var fileHIJTerms = new Dictionary <Int64[], Double>(new Extensions.IntArrayIEqualityComparer());
var fileHIJKLTerms = new Dictionary <Int64[], Double>(new Extensions.IntArrayIEqualityComparer());
var hamiltonian = new FermionHamiltonian();
var nOrbitals = 0L;
Match stringMisc = regexMiscellaneous.Match(line);
if (stringMisc.Success)
{
hamiltonian.MiscellaneousInformation = stringMisc.Groups["info"].ToString();
}
Match stringnuc = regexnuc.Match(line);
if (stringnuc.Success)
{
hamiltonian.EnergyOffset = Double.Parse(stringnuc.Groups["nuc"].ToString());
}
foreach (Match stringPQ in regexPQ.Matches(line))
{
if (stringPQ.Success)
{
var p = Int64.Parse(stringPQ.Groups["p"].ToString());
var q = Int64.Parse(stringPQ.Groups["q"].ToString());
var coeff = Double.Parse(stringPQ.Groups["coeff"].ToString());
var exponentString = stringPQ.Groups["exponent"].ToString();
var exponent = 0.0;
if (exponentString != "")
{
exponent = Double.Parse(stringPQ.Groups["exponent"].ToString());
}
nOrbitals = new long[] { nOrbitals, p + 1, q + 1 }.Max();
var orbitalIntegral = new OrbitalIntegral(new Int64[] { p, q }, coeff * (10.0).Pow(exponent));
var orbitalIntegralCanonical = orbitalIntegral.ToCanonicalForm();
//Logger.Message.WriteLine($"1e orbital { orbitalIntegral.Print()}, { orbitalIntegralCanonical.Print()}");
if (fileHIJTerms.ContainsKey(orbitalIntegralCanonical.OrbitalIndices))
{
// Check consistency
if (fileHIJTerms[orbitalIntegralCanonical.OrbitalIndices] != orbitalIntegral.Coefficient)
{
// Consistency check failed.
throw new System.NotSupportedException(
$"fileHPQTerm Consistency check fail. " +
$"Orbital integral {orbitalIntegral} coefficient {orbitalIntegral.Coefficient}" +
$"does not match recorded {orbitalIntegralCanonical} coefficient {fileHIJTerms[orbitalIntegral.OrbitalIndices]}.");
}
else
{
// Consistency check passed.
}
//Logger.Message.WriteLine($"1e orbital collision { orbitalIntegral.Print()}, { orbitalIntegralCanonical.Print()}");
}
else
{
fileHIJTerms.Add(orbitalIntegralCanonical.OrbitalIndices, orbitalIntegralCanonical.Coefficient);
}
}
}
foreach (Match stringPQRS in regexPQRS.Matches(line))
{
if (stringPQRS.Success)
{
var p = Int64.Parse(stringPQRS.Groups["p"].ToString());
var q = Int64.Parse(stringPQRS.Groups["q"].ToString());
var r = Int64.Parse(stringPQRS.Groups["r"].ToString());
var s = Int64.Parse(stringPQRS.Groups["s"].ToString());
var coeff = Double.Parse(stringPQRS.Groups["coeff"].ToString());
var exponentString = stringPQRS.Groups["exponent"].ToString();
var exponent = 0.0;
if (exponentString != "")
{
exponent = Double.Parse(stringPQRS.Groups["exponent"].ToString());
}
nOrbitals = new long[] { nOrbitals, p + 1, q + 1, r + 1, s + 1 }.Max();
var orbitalIntegral = new OrbitalIntegral(new Int64[] { p, q, r, s }, coeff * (10.0).Pow(exponent));
var orbitalIntegralCanonical = orbitalIntegral.ToCanonicalForm();
//Logger.Message.WriteLine($"2e orbital: { orbitalIntegral.Print()}, { orbitalIntegralCanonical.Print()}");
if (fileHIJKLTerms.ContainsKey(orbitalIntegralCanonical.OrbitalIndices))
{
// Check consistency
if (fileHIJKLTerms[orbitalIntegralCanonical.OrbitalIndices] != orbitalIntegral.Coefficient)
{
// Consistency check failed.
throw new System.NotSupportedException(
$"fileHPQRSTerm Consistency check fail. " +
$"Orbital integral {orbitalIntegral.OrbitalIndices} coefficient {orbitalIntegral.Coefficient}" +
$"does not match recorded {orbitalIntegralCanonical.OrbitalIndices} coefficient {fileHIJKLTerms[orbitalIntegral.OrbitalIndices]}.");
}
else
{
// Consistency check passed.
}
//Logger.Message.WriteLine($"2e orbital collision { orbitalIntegral.Print()}, { orbitalIntegralCanonical.Print()}");
}
else
{
fileHIJKLTerms.Add(orbitalIntegralCanonical.OrbitalIndices, orbitalIntegralCanonical.Coefficient);
}
}
}
hamiltonian.NOrbitals = nOrbitals;
foreach (var ijTerm in fileHIJTerms)
{
hamiltonian.AddFermionTerm(new OrbitalIntegral(ijTerm.Key, ijTerm.Value));
}
foreach (var ijklTerm in fileHIJKLTerms)
{
hamiltonian.AddFermionTerm(new OrbitalIntegral(ijklTerm.Key, ijklTerm.Value));
}
hamiltonian.SortAndAccumulate();
return(hamiltonian);
}
internal static ElectronicStructureProblem DeserializeSingleProblem(string line)
{
var problem = new ElectronicStructureProblem()
{
Metadata = new Dictionary <string, object>()
};
var regexMiscellaneous = new Regex(@"((info=(?<info>[^\s]*)))");
var regexnuc = new Regex(@"nuc=(?<nuc>-?\s*\d*.\d*)");
var regexPQ = new Regex(@"(^|\s+)(?<p>\d+),(?<q>\d+)\D*=\s*(?<coeff>-?\s*\d*.\d*)e?(?<exponent>-?\d*)");
var regexPQRS = new Regex(@"(^|\s+)(?<p>\d+)\D+(?<q>\d+)\D+(?<r>\d+)\D+(?<s>\d+)\D*=\s*(?<coeff>-?\s*\d*.\d*)e?(?<exponent>-?\d*)");
double coulombRepulsion = 0.0;
var fileHIJTerms = new Dictionary <int[], double>(new Extensions.ArrayEqualityComparer <int>());
var fileHIJKLTerms = new Dictionary <int[], double>(new Extensions.ArrayEqualityComparer <int>());
var hamiltonian = new OrbitalIntegralHamiltonian();
var nOrbitals = 0L;
Match stringMisc = regexMiscellaneous.Match(line);
if (stringMisc.Success)
{
problem.Metadata["misc_info"] = stringMisc.Groups["info"].ToString();
}
Match stringnuc = regexnuc.Match(line);
if (stringnuc.Success)
{
coulombRepulsion = double.Parse(stringnuc.Groups["nuc"].ToString()).ToDoubleCoeff();
hamiltonian.Add(TermType.OrbitalIntegral.Identity, new OrbitalIntegral(), coulombRepulsion);
}
foreach (Match stringPQ in regexPQ.Matches(line))
{
if (stringPQ.Success)
{
var p = int.Parse(stringPQ.Groups["p"].ToString());
var q = int.Parse(stringPQ.Groups["q"].ToString());
var coeff = double.Parse(stringPQ.Groups["coeff"].ToString());
var exponentString = stringPQ.Groups["exponent"].ToString();
var exponent = 0.0;
if (exponentString != "")
{
exponent = double.Parse(stringPQ.Groups["exponent"].ToString());
}
nOrbitals = new long[] { nOrbitals, p + 1, q + 1 }.Max();
var orbitalIntegral = new OrbitalIntegral(new int[] { p, q }, coeff * (10.0).Pow(exponent));
var orbitalIntegralCanonical = orbitalIntegral.ToCanonicalForm();
if (fileHIJTerms.ContainsKey(orbitalIntegralCanonical.OrbitalIndices))
{
// Check consistency
if (fileHIJTerms[orbitalIntegralCanonical.OrbitalIndices] != orbitalIntegral.Coefficient)
{
// Consistency check failed.
throw new System.NotSupportedException(
$"fileHPQTerm Consistency check fail. " +
$"Orbital integral {orbitalIntegral} coefficient {orbitalIntegral.Coefficient}" +
$"does not match recorded {orbitalIntegralCanonical} coefficient {fileHIJTerms[orbitalIntegral.OrbitalIndices]}.");
}
else
{
// Consistency check passed.
}
}
else
{
fileHIJTerms.Add(orbitalIntegralCanonical.OrbitalIndices, orbitalIntegralCanonical.Coefficient);
}
}
}
foreach (Match stringPQRS in regexPQRS.Matches(line))
{
if (stringPQRS.Success)
{
var p = int.Parse(stringPQRS.Groups["p"].ToString());
var q = int.Parse(stringPQRS.Groups["q"].ToString());
var r = int.Parse(stringPQRS.Groups["r"].ToString());
var s = int.Parse(stringPQRS.Groups["s"].ToString());
var coeff = double.Parse(stringPQRS.Groups["coeff"].ToString());
var exponentString = stringPQRS.Groups["exponent"].ToString();
var exponent = 0.0;
if (exponentString != "")
{
exponent = double.Parse(stringPQRS.Groups["exponent"].ToString());
}
nOrbitals = new long[] { nOrbitals, p + 1, q + 1, r + 1, s + 1 }.Max();
var orbitalIntegral = new OrbitalIntegral(new int[] { p, q, r, s }, coeff * (10.0).Pow(exponent));
var orbitalIntegralCanonical = orbitalIntegral.ToCanonicalForm();
if (fileHIJKLTerms.ContainsKey(orbitalIntegralCanonical.OrbitalIndices))
{
// Check consistency
if (fileHIJKLTerms[orbitalIntegralCanonical.OrbitalIndices] != orbitalIntegral.Coefficient)
{
// Consistency check failed.
throw new System.NotSupportedException(
$"fileHPQRSTerm Consistency check fail. " +
$"Orbital integral {orbitalIntegral.OrbitalIndices} coefficient {orbitalIntegral.Coefficient}" +
$"does not match recorded {orbitalIntegralCanonical.OrbitalIndices} coefficient {fileHIJKLTerms[orbitalIntegral.OrbitalIndices]}.");
}
else
{
// Consistency check passed.
}
}
else
{
fileHIJKLTerms.Add(orbitalIntegralCanonical.OrbitalIndices, orbitalIntegralCanonical.Coefficient);
}
}
}
hamiltonian.Add(fileHIJTerms.Select(o => new OrbitalIntegral(o.Key, o.Value)).ToList());
hamiltonian.Add(fileHIJKLTerms.Select(o => new OrbitalIntegral(o.Key, o.Value)).ToList());
problem.OrbitalIntegralHamiltonian = hamiltonian;
problem.NOrbitals = System.Convert.ToInt32(nOrbitals);
problem.CoulombRepulsion = coulombRepulsion.WithUnits("hartree");
return(problem);
}