Order(N) calculations

The Ordern(N) subsystem is quite fragile and only works for systems with clearly separated occupied and empty states. Note also that the option to compute the chemical potential automatically does not yet work in parallel.

ON.functional

(string): Choice of order-N minimization functionals:

• Kim: Functional of Kim, Mauri and Galli, PRB 52, 1640 (1995).
• Ordejon-Mauri: Functional of Ordejón et al, or Mauri et al, see PRB 51, 1456 (1995). The number of localized wave functions (LWFs) used must coincide with $N_{el}/2$ (unless spin polarized). For the initial assignment of LWF centers to atoms, atoms with even number of electrons, n, get n/2 LWFs. Odd atoms get (n+1)/2 and (n-1)/2 in an alternating sequence, ir order of appearance (controlled by the input in the atomic coordinates block).

• files: Reads localized-function information from a file and chooses automatically the functional to be used.

Use: Used only if SolutionMethod = ordern

Default value: Kim

ON.MaxNumIter

(integer): Maximum number of iterations in the conjugate minimization of the electronic energy, in each SCF cycle.

Use: Used only if SolutionMethod = OrderN

Default value: 1000

ON.etol

(real): Relative-energy tolerance in the conjugate minimization of the electronic energy. The minimization finishes if $2 (E_n - E_{n-1}) / (E_n + E_{n-1}) \leq$ ON.etol.

Use: Used only if SolutionMethod = OrderN

Default value: ${\tt 10^{-8}}$

ON.eta

(real energy): Fermi level parameter of Kim et al.. This should be in the energy gap, and tuned to obtain the correct number of electrons. If the calculation is spin polarised, then separate Fermi levels for each spin can be specified.

Use: Used only if SolutionMethod = OrderN

Default value: 0.0 eV

ON.eta_alpha

(real energy): Fermi level parameter of Kim et al. for alpha spin electrons. This should be in the energy gap, and tuned to obtain the correct number of electrons. Note that if the Fermi level is not specified individually for each spin then the same global eta will be used.

Use: Used only if SolutionMethod = OrderN

Default value: 0.0 eV

ON.eta_beta

(real energy): Fermi level parameter of Kim et al. for beta spin electrons. This should be in the energy gap, and tuned to obtain the correct number of electrons. Note that if the Fermi level is not specified individually for each spin then the same global eta will be used.

Use: Used only if SolutionMethod = OrderN

Default value: 0.0 eV

ON.RcLWF

(real legth): Localization redius for the Localized Wave Functions (LWF's).

Use: Used only if SolutionMethod = OrderN

Default value: 9.5 Bohr

ON.ChemicalPotential

(logical): Specifies whether to calculate an order-N estimate of the Chemical Potential, by the projection method (Goedecker and Teter, PRB 51, 9455 (1995); Stephan, Drabold and Martin, PRB 58, 13472 (1998)). This is done by expanding the Fermi function (or density matrix) at a given temperature, by means of Chebyshev polynomials, and imposing a real space truncation on the density matrix. To obtain a realistic estimate, the temperature should be small enough (typically, smaller than the energy gap), the localization range large enough (of the order of the one you would use for the Localized Wannier Functions), and the order of the polynomial expansion sufficiently large (how large depends on the temperature; typically, 50-100).

Use: Used only if SolutionMethod = OrderN.

Default value: .false.

Note: This option does not work in parallel. An alternative is to obtain the approximate value of the chemical potential using an initial diagonalization.

ON.ChemicalPotentialUse

(logical): Specifies whether to use the calculated estimate of the Chemical Potential, instead of the parameter ON.eta for the order-N energy functional minimization. This is useful if you do not know the position of the Fermi level, typically in the beginning of an order-N run.

Use: Used only if SolutionMethod = OrderN. Overrides the value of ON.eta. Overrides the value of ON.ChemicalPotential, setting it to .true..

Default value: .false.

Note: This option does not work in parallel. An alternative is to obtain the approximate value of the chemical potential using an initial diagonalization.

ON.ChemicalPotentialRc

(real length): Defines the cutoff radius for the density matrix or Fermi operator in the calculation of the estimate of the Chemical Potential.

Use: Used only if SolutionMethod = OrderN and ON.ChemicalPotential or ON.ChemicalPotentialUse = .true.

Default value: 9.5 Bohr.

ON.ChemicalPotentialTemperature

(real temperature or energy): Defines the temperature to be used in the Fermi function expansion in the calculation of the estimate of the Chemical Potential. To have an accurate results, this temperature should be smaller than the gap of the system.

Use: Used only if SolutionMethod = OrderN, and ON.ChemicalPotential or ON.ChemicalPotentialUse = .true.

Default value: 0.05 Ry.

ON.ChemicalPotentialOrder

(integer): Order of the Chebishev expansion to calculate the estimate of the Chemical Potential.

Use: Used only if SolutionMethod = OrderN, and ON.ChemicalPotential or ON.ChemicalPotentialUse = .true.

Default value: 100

ON.LowerMemory

(logical): If .true., then a slightly reduced memory algorithm is used in the 3-point line search during the order N minimisation. Only affects parallel runs.

Use: Used only if SolutionMethod = OrderN

Default value: .false.

Output of localized wavefunctions

At the end of each conjugate gradient minimization of the energy functional, the LWF's are stored on disk. These can be used as an input for the same system in a restart, or in case something goes wrong. The LWF's are stored in sparse form in file SystemLabel.LWF

It is important to keep very good care of this file, since the first minimizations can take MANY steps. Loosing them will mean performing the whole minimization again. It is also a good practice to save it periodically during the simulation, in case a mid-run restart is necessary.

ON.UseSaveLWF

(logical): Instructs to read the localized wave functions stored in file SystemLabel.LWF by a previous run.

Use: Used only if SolutionMethod is OrderN. If the required file does not exist, a warning is printed but the program does not stop. Overrides UseSaveData.

Default value: .false.