9. Nomenclature

The source code uses various nomenclatures for variables for easier reading and understanding. The most common variables and their meaning will be listed here. Some variables not listed here are explained in docstrings. Since most variables are ndarrays the respective shape will be displayed as well. If the variable is not a ndarray, the respective datatype will be shown. If the list is indexed over k-points it will be labeled as list over k.

9.1. Atoms variables

Variable	Meaning	Type/Shape
Natoms	Number of atoms	int
Z	Nuclei charges per atom	(Natoms)
Ns	Number of real-space grid points	int
s	Real-space grid points	(3)
r	Real-space sampling points	(Ns, 3)
G	Reciprocal space sampling points	(Number of G-vectors, 3)
G2	Squared G-vectors	(Number of G-vectors)
Gk2	Squared G+k-vectors	list over k + 1 [(Number of G-vectors)]
active	Indices for a selection of G+k-vectors	list over k + 1 [(Number of active G-vectors)]
G2c	Selected squared G-vectors	(Number of active G-vectors)
Gk2c	Selected squared G+k-vectors	list over k + 1 [(Number of active G-vectors)]
Sf	Structure factor per atom	(Natoms, Number of active G-vectors)

The variables of the Atoms object are explained here: Atoms.

The variables of the Occupations object are documented here: Occupations.

The variables of the KPoints object are documented here: KPoints.

9.2. Field variables

Variable	Meaning	Shape
n	Real-space electronic density	(Ns)
n_spin	Real-space spin densities	(Nspin, Ns)
dn_spin	Real-space gradients per axis of spin densities	(Nspin, Ns, 3)
tau	Real-space spin kinetic energy densities	(Nspin, Ns)
n_single	Real-space single-particle density	(Ns)
zeta	Real-space relative spin polarization	(Ns)
W	Reciprocal space unconstrained wave functions	list over k [(Nspin, Number of active G-vectors, Nstate)]
Y	Reciprocal space constrained wave functions	list over k [(Nspin, Number of active G-vectors, Nstate)]
Z	Reciprocal space unconstrained unoccupied wave functions	list over k [(Nspin, Number of active G-vectors, Nempty)]
D	Reciprocal space constrained unoccupied wave functions	list over k [(Nspin, Number of active G-vectors, Nempty)]
Yrs	Real-space constrained wave functions	list over k [(Nspin, Ns, Nstate)]
psi	Reciprocal space Hamiltonian eigenstates	list over k [(Nspin, Number of active G-vectors, Nstate)]
phi	Real-space electrostatic Hartree field	(Ns)
exc	Real-space exchange-correlation energy density	(Ns)
vxc	Real-space exchange-correlation potential (dexc/dn)	(Nspin, Ns)
vsigma	Real-space gradient-dependent potential contribution (n dexc/d|dn|^2)	(1 or 3, Ns)
vtau	Real-space tau-dependent potential contribution (dexc/dtau)	(1 or 3, Ns)
Vloc	Reciprocal space local pseudopotential contribution	(Number of active G-vectors)
Vnonloc	Reciprocal space non-local pseudopotential contribution	(Nspin, Number of active G-vectors, Nstate)
kso	Real-space Kohn-Sham orbitals	list over k [(Nspin, Ns, Nstate)]
fo	Real-space Fermi orbitals	list [(Nspin, Ns, Nstate)]
flo	Real-space Fermi-Löwdin orbitals	list [(Nspin, Ns, Nstate)]
wo	Real-space Wannier orbitals	list [(Nspin, Ns, Nstate)]
scdm	Real-space orbitals localized via the SCDM method	list [(Nspin, Ns, Nstate)]

The variables of the SCF object are explained here: SCF.

The variables of the Energy object are documented here: Energy.

9.3. Pseudopotential variables

Variable	Meaning	Type/Shape
GTH	Combination of GTH parameters for all atoms species	dict
psp	GTH parameters for one atom species	dict
NbetaNL	Number of projector functions	int
betaNL	Atom-centered projector functions	(Number of active G-vectors, NbetaNL)
prj2beta	Map projector functions to atom species data	(3, Natoms, 4, 7)

The GTH variables are listed here: GTH.

9.4. Miscellaneous variables

Variable	Meaning	Type/Shape
Nk	Number of k-points	int
k	k-point coordinates	(Nk, 3)
wk	k-point weights	(Nk)
f	Occupation numbers per spin and state	(Nk, Nspin, Nstate)
F	Diagonal matrix of occupation numbers	list over k [(Nspin, Nstate, Nstate)]
U	Overlap of wave functions	(Nstate, Nstate)
epsilon	Eigenenergies	list over k [(Nspin, Nstate)]
fods	List of FOD positions	list [(Number of up-FODs, 3), (Number of down-FODs, 3)]
elec_symbols	List of FOD identifier atoms	list

The configuration variables are listed here: ConfigClass.