nanotools.mix module

This module defines the Mix class.

class nanotools.mix.Mix(alpha: float = 0.2, converged: bool = False, eres=None, etol: float = 1e-08, imem: int = 20, pp_period: int = 3, iter: int = 0, maxit: int = 100, method: str = 'pul', metric: str = 'eye', monitored_variables: list = [1], precond: str = 'eye', res=None, tol: float = 1e-08, type: str = 'den')

Bases: Base

Mix class.

alpha

Mixing fraction. alpha should be a parameter in the interval [0, 1]. The closer it is to 0, the more stable the convergence of the solver. The closer it is to 1, the faster the convergence of the solver.

Examples:

mix.alpha = 0.45

Type:

float

eres

On exit, array containing the total energy residuals.

Type:

float

etol

Total energy tolerance (in Hartree / electron).

Type:

float

imem

Maximal number of trial functions retained to compute the new trial function in the mixer. For example, in a calculation doing density mixing with mix.imem = 10, the mixer will estimate the next trial density based on the densities of the last 10 iterations.

Examples:

mix.imem = 10

Type:

int

pp_period

Period of the periodic Pulay mixer, namely one less than the number of linear mixing steps between Pulay mixing steps. Only used if mix.method = “per”.

Examples:

mix.pp_period = 3

Type:

int

maxit

Maximal number of iterations. Note that the Kohn-Sham solver will return an answer even if it has not converged, which can then be use for restart.

Examples:

mix.maxit = 50

Type:

int

method

method takes the following values:

• “lin”: linear mixing.

• “pul”: Pulay mixing.

• “per”: Periodic Pulay mixing.

Examples:

mix.method = "pul"

Type:

str

metric

Quasi-Newton methods perform inner products, which can be calculated straightforwardly using the identity metric (“eye”). Kresse and Furthmuller have however suggested using the Kerker metric (“ker”) .

metric takes the following values:

• eye: identity metric.

• ker: Kerker-like metric

Examples:

mix.metric = "eye"

Type:

str

monitored_variables

Array of integer giving which variables are monitored and used to determine convergence.

• 1: monitor density.

• 2: monitor total energy.

Examples:

mix.monitored_variables = [1] # monitor the density residual
mix.monitored_variables = [2] # monitor the total energy residual
mix.monitored_variables = [1, 2] # monitor both residuals

Type:

list of int

precond

Initial inverse Jacobian. The initial inverse Jacobian is necessary in quasi-Newton methods. It is by default “eye” (the identity), in which case the initial inverse Jacobian is alpha I, where alpha = mix.alpha. It can also be “ker” (for Kerker).

Examples:

mix.precond = "ker"

Type:

str

res

On exit, array containing the density residuals.

Type:

float

tol

In self-consistent calculations, the convergence procedure stops if the change in density per electron becomes smaller than tol. In equations,

\[\delta d = \int \|d_{i}^{out} - d_{i}^{in}\| / N^{el}.\]

Examples:

mix.tol = 1e-6

Type:

float

type

Determine which quantity to mix. Only density (“den”) can be mixed currently.

Examples:

mix.type = "den"

Type:

str

set_alpha(alpha)

Sets the mixing fraction.

alpha should be a parameter in the interval [0, 1]. The closer it is to 0, the more stable the convergence of the solver. The closer it is to 1, the faster the convergence of the solver.

set_etol(tol)

Sets the total energy tolerance. The tolerance is in Hartree per electron.

set_imem(imem)

Sets the mixer memory.

Maximal number of trial functions retained to compute the new trial function in the mixer. For example, in a calculation doing density mixing with mix.imem = 10, the mixer will estimate the next trial density based on the densities of the last 10 iterations.

set_maxit(maxit)

Sets the maximal number of iterations.

Maximal number of iterations. Note that the Kohn-Sham solver will return an answer even if it has not converged, which can then be use for restart.

set_method(method)

Sets the mixing method.

method takes the following values:

• “lin”: linear mixing.

• “pul”: Pulay mixing.

• “per”: Periodic Pulay mixing.

set_metric(metric)

Sets the mixing metric.

Quasi-Newton methods perform inner products, which can be calculated straightforwardly using the identity metric (“eye”). Kresse and Furthmuller have however suggested using the Kerker metric (“ker”) .

metric takes the following values:

• eye: identity metric.

• ker: Kerker-like metric.

set_monitored_variables(var, tol=None)

Sets the monitored variables. Allowed values are “density” and “energy”.

set_pp_period(pp_period)

Sets the period of the periodic Pulay mixer.

Period of the periodic Pulay mixer, namely one less than the number of linear mixing steps between Pulay mixing steps. Only used if mix.method = "per".

set_precond(precond)

Sets the mixing precond.

The mixing preconditioner is an initial guess for the inverse Jacobian. The initial inverse Jacobian is necessary in quasi-Newton methods. It is by default “eye” (for identity), in which case the initial inverse Jacobian is alpha I, where alpha = mix.alpha. It can also be “ker” (for Kerker).

precond takes the following values:

• eye: identity precond.

• ker: Kerker precond.

set_tol(tol)

Sets the density tolerance. The tolerance is in electron per electron.

set_type(type)

Sets the mixing type.

Determines which quantity to mix. Only density (“den”) can be mixed currently.