internal void SetWavefunctions(KPoint otherPt, SymmetryList symmetries, List <int> orbitalMap)
{
if (this.wfk.Count != 0)
{
throw new InvalidOperationException();
}
for (int n = 0; n < otherPt.Wavefunctions.Count; n++)
{
var otherWfk = otherPt.Wavefunctions[n];
var wfk = new Wavefunction(otherWfk.Coeffs.Length);
wfk.Energy = otherWfk.Energy;
wfk.FermiFunction = otherWfk.FermiFunction;
for (int k = 0; k < otherWfk.Coeffs.Length; k++)
{
int newOrb = symmetries.TransformOrbital(orbitalMap, k);
System.Diagnostics.Debug.Assert(wfk.Coeffs[newOrb] == 0);
wfk.Coeffs[newOrb] = otherWfk.Coeffs[k];
}
this.wfk.Add(wfk);
}
}
void CreateBands(TightBinding tb, string name)
{
using (StreamReader r = new StreamReader(name))
{
string line = r.ReadLine();
if (line != "# Grid")
{
Console.WriteLine("Not an eigenvalues file!");
System.Environment.Exit(3);
}
int[] grid = new int[3];
int[] shift = new int[3];
ParseGrid(grid, shift, line);
if (line != "# Eigenvalues")
{
Console.WriteLine("Not an eigenvalues file!");
System.Environment.Exit(2);
}
KptList kpts = new KptList();
kpts.Mesh = grid;
kpts.Shift = shift;
while (r.EndOfStream == false)
{
line = r.ReadLine();
string[] elements = line.Split(new char[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
KPoint kpt = new KPoint(new Vector3(double.Parse(elements[0]),
double.Parse(elements[1]),
double.Parse(elements[2])));
for (int i = 3; i < elements.Length; i++)
{
Wavefunction wfk = new Wavefunction(0);
wfk.Energy = double.Parse(elements[i]);
kpt.Wavefunctions.Add(wfk);
}
kpts.Kpts.Add(kpt);
}
CreateTetrahedronMesh(kpts);
string outputfile = name + ".bands";
using (StreamWriter w = new StreamWriter(outputfile))
{
WriteBands(tb, kpts, w);
}
}
}
internal void SetWavefunctions(Matrix eigenvals, Matrix eigenvecs)
{
for (int n = 0; n < eigenvals.Rows; n++)
{
var wfk = new Wavefunction(eigenvecs.Rows);
wfk.Energy = eigenvals[n, 0].RealPart;
for (int c = 0; c < eigenvecs.Rows; c++)
{
wfk.Coeffs[c] = eigenvecs[c, n];
}
this.wfk.Add(wfk);
}
}
private Matrix[] CalcGreenFunction(TightBindingSuite.TightBinding tb, RpaParams p, KptList kmesh)
{
int orbitalCount = tb.Orbitals.Count;
Matrix[] retval = new Matrix[kmesh.Kpts.Count];
Complex denomFactor = new Complex(0, p.Temperature);
for (int k = 0; k < kmesh.Kpts.Count; k++)
{
retval[k] = new Matrix(orbitalCount, orbitalCount);
Matrix hamilt = tb.CalcHamiltonian(kmesh.Kpts[k].Value);
Matrix vals, vecs;
hamilt.EigenValsVecs(out vals, out vecs);
for (int i = 0; i < orbitalCount; i++)
{
for (int j = 0; j < orbitalCount; j++)
{
for (int n = 0; n < orbitalCount; n++)
{
var wfk = new Wavefunction(orbitalCount);
wfk.Energy = vals[n, 0].RealPart;
for (int c = 0; c < vecs.Rows; c++)
{
wfk.Coeffs[c] = vecs[c, n];
}
Complex coeff =
wfk.Coeffs[i].Conjugate() *
wfk.Coeffs[j];
Complex g = 1.0 / (p.Frequency + p.ChemicalPotential - wfk.Energy + denomFactor);
retval[k][i, j] += g * coeff;
}
}
}
}
return retval;
}
private Matrix[] CalcGreenFunction(TightBindingSuite.TightBinding tb, RpaParams p, KptList kmesh)
{
int orbitalCount = tb.Orbitals.Count;
Matrix[] retval = new Matrix[kmesh.Kpts.Count];
Complex denomFactor = new Complex(0, p.Temperature);
for (int k = 0; k < kmesh.Kpts.Count; k++)
{
retval[k] = new Matrix(orbitalCount, orbitalCount);
Matrix hamilt = tb.CalcHamiltonian(kmesh.Kpts[k].Value);
Matrix vals, vecs;
hamilt.EigenValsVecs(out vals, out vecs);
for (int i = 0; i < orbitalCount; i++)
{
for (int j = 0; j < orbitalCount; j++)
{
for (int n = 0; n < orbitalCount; n++)
{
var wfk = new Wavefunction(orbitalCount);
wfk.Energy = vals[n, 0].RealPart;
for (int c = 0; c < vecs.Rows; c++)
{
wfk.Coeffs[c] = vecs[c, n];
}
Complex coeff =
wfk.Coeffs[i].Conjugate() *
wfk.Coeffs[j];
Complex g = 1.0 / (p.Frequency + p.ChemicalPotential - wfk.Energy + denomFactor);
retval[k][i, j] += g * coeff;
}
}
}
}
return retval;
}
public Wavefunction Clone(List<int> orbitalMap)
{
Wavefunction retval = new Wavefunction(coeffs.Length);
retval.Energy = Energy;
retval.FermiFunction = FermiFunction;
if (orbitalMap != null && orbitalMap.Count > 0)
{
for (int i = 0; i < coeffs.Length; i++)
{
retval.coeffs[orbitalMap[i]] = coeffs[i];
}
}
else
retval.coeffs = (Complex[])coeffs.Clone();
return retval;
}
public Wavefunction Clone(List <int> orbitalMap)
{
Wavefunction retval = new Wavefunction(coeffs.Length);
retval.Energy = Energy;
retval.FermiFunction = FermiFunction;
if (orbitalMap != null && orbitalMap.Count > 0)
{
for (int i = 0; i < coeffs.Length; i++)
{
retval.coeffs[orbitalMap[i]] = coeffs[i];
}
}
else
{
retval.coeffs = (Complex[])coeffs.Clone();
}
return(retval);
}
void DoDensityOfStates()
{
KptList ks = KMesh;
using (StreamWriter outf = new StreamWriter(outputfile + ".dos"))
{
double smearing = TemperatureMesh[0];
double effBeta = 1 / smearing;
double emin = double.MaxValue, emax = double.MinValue;
for (int i = 0; i < ks.Kpts.Count; i++)
{
KPoint kpt = ks.Kpts[i];
emin = Math.Min(emin, kpt.Wavefunctions.Min(x => x.Energy));
emax = Math.Max(emax, kpt.Wavefunctions.Max(x => x.Energy));
}
emin -= smearing * 10;
emax += smearing * 10;
emin -= MuMesh[0];
emax -= MuMesh[0];
int epts = 3000;
double[] energyGrid = new double[epts];
double[,] dos = new double[epts, Orbitals.Count + 1];
int zeroIndex = 0;
Output.WriteLine(
"Calculating DOS from {0} to {1} with finite temperature smearing {2}.",
emin, emax, smearing);
Output.WriteLine("Using {0} kpts.", ks.Kpts.Count);
for (int i = 0; i < epts; i++)
{
energyGrid[i] = emin + (emax - emin) * i / (double)(epts - 1);
if (energyGrid[i] < 0)
{
zeroIndex = i;
}
}
for (int i = 0; i < ks.Kpts.Count; i++)
{
KPoint kpt = ks.Kpts[i];
for (int j = 0; j < kpt.Wavefunctions.Count; j++)
{
Wavefunction wfk = kpt.Wavefunctions[j];
double energy = wfk.Energy - MuMesh[0];
int startIndex = FindIndex(energyGrid, energy - smearing * 10);
int endIndex = FindIndex(energyGrid, energy + smearing * 10);
for (int k = startIndex; k <= endIndex; k++)
{
double ferm = FermiFunction(energyGrid[k], energy, effBeta);
double smearWeight = ferm * (1 - ferm) * effBeta;
smearWeight *= ks.Kpts[i].Weight;
double weight = 0;
for (int l = 0; l < wfk.Coeffs.Length; l++)
{
if (PoleStates.Contains(l))
{
continue;
}
double stateval = wfk.Coeffs[l].MagnitudeSquared;
weight += stateval;
}
if (PoleStates.Count == 0 && Math.Abs(weight - 1) > 1e-8)
{
throw new Exception("Eigenvector not normalized!");
}
dos[k, 0] += smearWeight * weight;
for (int state = 0; state < wfk.Coeffs.Length; state++)
{
if (PoleStates.Contains(state))
{
continue;
}
double wtk = wfk.Coeffs[state].MagnitudeSquared;
dos[k, state + 1] += smearWeight * wtk;
}
}
}
}
// symmetrize DOS for equivalent orbitals.
for (int k = 0; k < epts; k++)
{
for (int i = 0; i < Orbitals.Count; i++)
{
double wtk = dos[k, i + 1];
int count = 1;
foreach (int equiv in Orbitals[i].Equivalent)
{
wtk += dos[k, equiv + 1];
count++;
}
dos[k, i + 1] = wtk / count;
foreach (int equiv in Orbitals[i].Equivalent)
{
dos[k, equiv + 1] = wtk / count;
}
}
}
if (emin < 0 && emax > 0)
{
if (zeroIndex + 1 >= energyGrid.Length)
{
zeroIndex = energyGrid.Length - 2;
}
double slope = (dos[zeroIndex, 0] - dos[zeroIndex + 1, 0]) / (energyGrid[zeroIndex] - energyGrid[zeroIndex + 1]);
double dosEF = slope * (-energyGrid[zeroIndex]) + dos[zeroIndex, 0];
Output.WriteLine("Density of states at chemical potential: {0}", dosEF);
for (int i = 0; i < epts; i++)
{
outf.Write("{0} ", energyGrid[i]);
for (int j = 0; j < Orbitals.Count + 1; j++)
{
outf.Write("{0} ", dos[i, j]);
}
outf.WriteLine();
}
}
}
}
Matrix CalcX0(TightBinding tb, double freq, Vector3 q)
{
int orbitalCount = tb.Orbitals.Count;
int size = orbitalCount * orbitalCount;
Matrix x = new Matrix(size, size);
Complex denom_factor = new Complex(0, 1e-4);
//StreamWriter w = new StreamWriter(string.Format("qcont.{0}", q.ToString("0.000")));
//bool writeThis = false;
for (int l1 = 0; l1 < orbitalCount; l1++)
{
for (int l4 = 0; l4 < orbitalCount; l4++)
{
for (int l3 = l1; l3 < orbitalCount; l3++)
{
for (int l2 = l4; l2 < orbitalCount; l2++)
{
int i = GetIndex(tb, l1, l2);
int j = GetIndex(tb, l3, l4);
bool foundSymmetry = false;
//if (l1 == 0 && l2 == 0 && l3 == 0 && l4 == 0)
// writeThis = true;
//else
//writeThis = false;
//if (writeThis)
// w.WriteLine("{0}{1}{2}{3}", l1, l2, l3, l4);
for (int s = 0; s < tb.Symmetries.Count; s++)
{
Symmetry sym = tb.Symmetries[s];
if (sym.OrbitalTransform == null || sym.OrbitalTransform.Count == 0)
{
continue;
}
int newL1 = sym.OrbitalTransform[l1];
int newL2 = sym.OrbitalTransform[l2];
int newL3 = sym.OrbitalTransform[l3];
int newL4 = sym.OrbitalTransform[l4];
int newI = GetIndex(tb, newL1, newL2);
int newJ = GetIndex(tb, newL3, newL4);
if (newI == i && newJ == j)
{
continue;
}
foundSymmetry = true;
if (newL1 > l1)
{
foundSymmetry = false;
}
if (newL2 > l2)
{
foundSymmetry = false;
}
if (newL3 > l3)
{
foundSymmetry = false;
}
if (newL4 > l4)
{
foundSymmetry = false;
}
if (foundSymmetry)
{
x[i, j] = x[newI, newJ];
x[j, i] = x[i, j].Conjugate();
break;
}
}
if (foundSymmetry)
{
continue;
}
Complex total = 0;
for (int allkindex = 0; allkindex < tb.KMesh.AllKpts.Count; allkindex++)
{
Complex val = 0;
Vector3 k = tb.KMesh.AllKpts[allkindex];
Vector3 kq = k + q;
//List<int> kOrbitalMap;
//List<int> kqOrbitalMap;
//int kindex = tb.KMesh.IrreducibleIndex(k, tb.Lattice, tb.Symmetries, out kOrbitalMap);
//int kqindex = tb.KMesh.IrreducibleIndex(kq, tb.Lattice, tb.Symmetries, out kqOrbitalMap);
int kindex = tb.KMesh.AllKindex(k, tb.Lattice);
int kqindex = tb.KMesh.AllKindex(kq, tb.Lattice);
System.Diagnostics.Debug.Assert(kindex == allkindex);
//int newL1 = TransformOrbital(kqOrbitalMap, l1);
//int newL2 = TransformOrbital(kOrbitalMap, l2);
//int newL3 = TransformOrbital(kqOrbitalMap, l3);
//int newL4 = TransformOrbital(kOrbitalMap, l4);
for (int n1 = 0; n1 < orbitalCount; n1++)
{
Wavefunction wfk = Bands(tb, kindex, n1);
double e1 = wfk.Energy;
double f1 = wfk.FermiFunction;
for (int n2 = 0; n2 < orbitalCount; n2++)
{
Wavefunction wfq = Bands(tb, kqindex, n2);
double e2 = wfq.Energy;
double f2 = wfq.FermiFunction;
Complex coeff =
wfq.Coeffs[l1] * wfq.Coeffs[l4].Conjugate() *
wfk.Coeffs[l3] * wfk.Coeffs[l2].Conjugate();
if (coeff == 0)
{
continue;
}
if (f1 < 1e-15 && f2 < 1e-15)
{
continue;
}
Complex denom_p = (e2 - e1 + freq + denom_factor);
//Complex denom_n = (e2 - e1 - freq - denom_factor);
//Complex lindhard = (f1 - f2) * (1.0 / denom_p + 1.0 / denom_n);
Complex lindhard = (f1 - f2) * (1.0 / denom_p);
Complex contrib = coeff * lindhard;
if (Math.Abs(f1 - f2) < 1e-11 && freq == 0.0)
{
contrib = coeff * f1 * (1 - f1) * Beta;
}
//w.Write("{0} {1} {2} {3} ", kindex, kqindex, n1, n2);
//w.WriteLine("{0} {1} {2} {3} {4}", coeff, e1, e2, f1, f2);
if (double.IsNaN(contrib.RealPart) || double.IsNaN(contrib.ImagPart))
{
throw new Exception("Found NaN when evaluating X0");
}
val += contrib;
}
}
//w.WriteLine("{0} {1} total {2} + {3}i", kindex, kqindex,
// Math.Round(val.RealPart, 4), Math.Round(val.ImagPart, 4));
//Output.WriteLine(tb.KMesh.AllKpts[kindex].Weight.ToString());
val *= tb.KMesh.AllKpts[kindex].Weight;
total += val;
//if (writeThis)
// w.WriteLine("{0} {1} {2}", allkindex, total, val);
}
x[i, j] = total;
x[j, i] = total.Conjugate();
//if (writeThis)
//{
// w.WriteLine("total for {0}{1}{2}{3}: {4}", l1, l2, l3, l4, total);
// w.WriteLine("---------------------");
//}
}
}
}
}
//w.Close();
return(x);
}
internal void SetWavefunctions(KPoint otherPt, SymmetryList symmetries, List<int> orbitalMap)
{
if (this.wfk.Count != 0) throw new InvalidOperationException();
for (int n = 0; n < otherPt.Wavefunctions.Count; n++)
{
var otherWfk = otherPt.Wavefunctions[n];
var wfk = new Wavefunction(otherWfk.Coeffs.Length);
wfk.Energy = otherWfk.Energy;
wfk.FermiFunction = otherWfk.FermiFunction;
for (int k = 0; k < otherWfk.Coeffs.Length; k++)
{
int newOrb = symmetries.TransformOrbital(orbitalMap, k);
System.Diagnostics.Debug.Assert(wfk.Coeffs[newOrb] == 0);
wfk.Coeffs[newOrb] = otherWfk.Coeffs[k];
}
this.wfk.Add(wfk);
}
}
internal void SetWavefunctions(Matrix eigenvals, Matrix eigenvecs)
{
for (int n = 0; n < eigenvals.Rows; n++)
{
var wfk = new Wavefunction(eigenvecs.Rows);
wfk.Energy = eigenvals[n, 0].RealPart;
for (int c = 0; c < eigenvecs.Rows; c++)
{
wfk.Coeffs[c] = eigenvecs[c, n];
}
this.wfk.Add(wfk);
}
}
void CreateBands(TightBinding tb, string name)
{
using (StreamReader r = new StreamReader(name))
{
string line = r.ReadLine();
if (line != "# Grid")
{
Console.WriteLine("Not an eigenvalues file!");
System.Environment.Exit(3);
}
int[] grid = new int[3];
int[] shift = new int[3];
ParseGrid(grid, shift, line);
if (line != "# Eigenvalues")
{
Console.WriteLine("Not an eigenvalues file!");
System.Environment.Exit(2);
}
KptList kpts = new KptList();
kpts.Mesh = grid;
kpts.Shift = shift;
while (r.EndOfStream == false)
{
line = r.ReadLine();
string[] elements = line.Split(new char[] { ' '}, StringSplitOptions.RemoveEmptyEntries );
KPoint kpt = new KPoint(new Vector3(double.Parse(elements[0]),
double.Parse(elements[1]),
double.Parse(elements[2])));
for (int i = 3; i < elements.Length; i++)
{
Wavefunction wfk = new Wavefunction(0);
wfk.Energy = double.Parse(elements[i]);
kpt.Wavefunctions.Add(wfk);
}
kpts.Kpts.Add(kpt);
}
CreateTetrahedronMesh(kpts);
string outputfile = name + ".bands";
using (StreamWriter w = new StreamWriter(outputfile))
{
WriteBands(tb, kpts, w);
}
}
}