Convergence criteria

There are two parameters controlling the computation accuracy of the solution (listed in input file):

energyconveps           1.0e-6   # energy convergence epsilon
                                 # energy changes between two subsequent iteration 
                                 # expressed in units E_ffg needs to be smaller than npartconveps
                                 # for converged solution
                                 # default=1.0e-6
npartconveps            1.0e-6   # number of particles convergence epsilon
                                 # relative difference between obtained particle number
                                 # and total particle number must be smaller than npartconveps
                                 # for converged solution
                                 # default=1.0e-6

The solution is regarded as converged when all contributions to the energy satisfy energyconvep and particle number satisfies criteria npartconveps. Info about the status of convergence is printed on standard output. Example of a report for converged solution for input parameters:

Na                      17       # requested particle number, spin-a
Nb                      18       # requested particle number, spin-b
energyconveps           1.0e-6   # energy convergence epsilon
npartconveps            1.0e-6   # number of particles convergence epsilon

may look like:

# CONVERGENCE REPORT PARTICLE NUMBER: it=58
    SPINA: NEW=              17 OLD=       17.000003 DIFF=  -3.1644056e-06 CONVSTATUS=  PASS NPARTCONV=   2.1975596e-09
    SPINB: NEW=       18.000001 OLD=       17.999995 DIFF=   5.4727832e-06 CONVSTATUS=  PASS NPARTCONV=    2.406396e-08
# CONVERGENCE REPORT ENERGY: it=58
    E_kin: NEW=        1.879979 OLD=       1.8799781 DIFF=   8.9986865e-07 CONVSTATUS=  PASS
    E_pot: NEW=     -0.51360103 OLD=     -0.51360098 DIFF=  -4.7134213e-08 CONVSTATUS=  PASS
   E_pair: NEW=     -0.94237189 OLD=     -0.94237177 DIFF=  -1.2408755e-07 CONVSTATUS=  PASS
   E_curr: NEW=   3.5892537e-14 OLD=   9.6882531e-14 DIFF=  -6.0989994e-14 CONVSTATUS=  PASS
 E_potext: NEW=               0 OLD=               0 DIFF=               0 CONVSTATUS=  PASS
E_pairext: NEW=               0 OLD=               0 DIFF=               0 CONVSTATUS=  PASS
 E_velext: NEW=               0 OLD=               0 DIFF=               0 CONVSTATUS=  PASS
  ------------------------------------------------------------------------------------------
    E_tot: NEW=      0.42400609 OLD=      0.42400536 DIFF=   7.2864682e-07 CONVSTATUS=  PASS

Ajusting of chemical potentials

Static codes adjust chemical potentials automatically in such way to provide a solution with requested particle number. Following parameters control adjusting process:

muchange                0.5      # coefficient for changing chemical potential, default=0.5
mumaxchange             0.05     # maximal allowed changed of chemical potential per iteration,
                                 # in units of Fermi energy

Chemical potentials are adjusted according to rule:

\begin{aligned}
\Delta\mu_{\sigma}^{(i)} &= \textrm{muchange}\,\frac{N_{\sigma}^{(\textrm{req.})}-N_{\sigma}^{(i)}}{N_{\sigma}^{(\textrm{req.})}}\\
\textrm{if}\,|\Delta\mu_{\sigma}^{(i)}/\varepsilon_F|&>\textrm{mumaxchange}:\,\textrm{decrease}\,\textrm{magnitude}\,\textrm{of}\,\Delta\mu_{\sigma}^{(i)}\\
\mu_{\sigma}^{(i+1)} &= \mu_{\sigma}^{(i+1)} + \Delta\mu_{\sigma}^{(i)} 
\end{aligned}