calculateTotalEnergy

	Core NanoLanguage elements
calculateOptimizedAtomicGeometry	eigenstateOccupationParameters

Name

calculateTotalEnergy — Calculates the total energy of a system.

Synopsis

Namespace: ATK.KohnSham or ATK.TwoProbe

PhysicalQuantity calculateTotalEnergy(self_consistent_calculation)

Description

This function calculates and returns the Total Energy of the system. The total energy is calculated as a sum of different contributions. By default, only the value of the total energy is returned. In order to get more information on the single contributions, the global verbosity level can be set to 10. In this case, the function will also print on the output a more detailed breakdown of the various terms that contribute to the total energy. For a verbosity level below 10, nothing is printed when the function is called.

List of arguments

self_consistent_calculation

An object returned from a previously performed self-consistent calculation.

Default: None

Usage examples

from ATK.KohnSham import *
...
dft_calculation = dft_method.apply(...)
energy = calculateTotalEnergy( dft_calculation )
print "Total energy: %s eV" % (energy.inUnitsOf(eV))

To obtain more detailed information about the total energy:

import ATK
ATK.setVerbosityLevel(10)
...
energy = calculateTotalEnergy( dft_calculation )
print energy

which will produce an output similar to the following:

# ----------------------------------------------------------------
# Total Energy           = -865.3068 eV
# Potential Energy       = -865.3068 eV
# Ion Kinetic Energy     = 0.0000 eV
# ----------------------------------------------------------------
# NumOrb: Energy of system
# ----------------------------------------------------------------
# Charge                  = 12.0000
# Band Structure Energy   = -179.6787 eV
# ----------------------------------------------------------------
# El. Kinetic Energy      = 593.1333 eV
# NL Energy               = -189.0527 eV
# dEna                    = 3.5017 eV
# dUscf                   = 0.4447 eV
# XC Energy               = -193.3035 eV
# ENA                     = 114.2218 eV
# Eions                   = -1194.2521 eV
# ----------------------------------------------------------------
# Electron kinetic energy = 593.1333 eV
# Electrostatic energy    = -1265.1366 eV
# Exchange-corr. energy   = -193.3035 eV
# ----------------------------------------------------------------
# Total potential energy  = -865.3068 eV
# ----------------------------------------------------------------
-865.306766388 eV

Notes

Note, since ATK uses pseudo-potentials to represent the core electrons, the total energy itself has no real meaning. Only energy differences have physical relevance, being they between different states in the same system, or the same system calculated for different conditions (such as when relaxing the geometry).

Notes on the output

Setting the global verbosity level to 10, the function calculateTotalEnergy() prints information on the different energy contributions. For a more detailed definition of these contributions, please refer to [12]. The various terms are briefly presented in the following:

Total Energy = Potential Energy + Ion Kinetic Energy

Potential Energy = The potential energy of the system (including both ionic and electronic contributions).

Ion Kinetic Energy = The ionic kinetic energy.

For the calculations that presently can be performed in ATK, the ions are stationary, therefore, the resulting value for the Ion Kinetic Energy is 0.0000 eV. Thus, the total and potential energies are always identically equal.

The Potential Energy (also called Total potential energy) can be, in turn, separated in various terms:

Potential Energy = Electron kinetic energy + Electrostatic energy + Exchange-corr. energy

Electron kinetic energy = The kinetic energy of the non-interacting electron gas (also called El. Kinetic Energy).

Electrostatic energy = The mean-field electrostatic energy of the electron gas and the ions.

Exchange-corr. energy = The exchange-correlation energy of the electrons (also called XC Energy).

The individual contribution to the Electrostatic energy:

NL Energy, ENA, Eions, dEna, and dUscf

are also reported in the output, for the definition of these terms we remand to [12].

Apart from the Total Energy itself, the Charge in the system and the Band Structure Energy (i.e., the sum of the energies of all eigenstates, weighted with their occupation) are also printed.

The total charge in the system is conserved for molecular, bulk, and electrode systems. Note that for two-probe systems, the charge listed in the total energy output also contains the charges located in the two electrode unit cells as well, whereas the value of q as presented in the convergence information for the self-consistent cycle only counts the charges in the central region. As a consequence, these values will be different.

Further examples


calculateOptimizedAtomicGeometry		eigenstateOccupationParameters