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The default energy unit is Rydberg (Ry), and default distance unit is bohr.
The following are the common input keywords in this section, and must appear in the exact order indicated, if they appear. There are many mandatory keyword/data inputs. Optional keywords are enclosed in square brackets, e.g. [scale ].
| non-spin | spin-polarized | |
|---|---|---|
| CAPZ LDA | CAPZ LDA | CAPZSP LDA-SP |
| PBE GGA | PBE GGA | PBE-SP GGA-SP |
| PW91 | PW91 | PW91SP |
| BLYP | BLYP | BLYPSP |
| AM05 | AM05 | AM05SP |
The default (only) LDA functional is the Perder/Zunger parameterization
Important: the scale functions do not scale lattice vectors in
non-periodic directions, only along periodic directions. The
atomic positions may be scaled in the z-direction for a slab
calculation using the "scale " or 'scalez" keyword, but the third
lattice vector "C", the non-periodic lattice vector along the
z-axis is not scaled.
The lattice vectors along periodic directions will be determined by
the physics of the problem, but the lattice vectors in non-periodic
directions are determined by computational considerations.
First, note discussion above about dimension of system. For a ndim=2 slab
calculation, the slab normal must be along the z-axis,
and so must the third lattice vector "C".
For a ndim=1 chain, the periodic direction
(given by the first lattice vector "A") must be the x-direction,
and the last two lattice vectors, B and C, must be in the y-z plane.
The extent of the non-periodic lattice vectors must be large enough to
contain the charge density of the system. A good rule of thumb is
that charge density extends 10-12 bohr around an atom. Hence, lattice
vectors should be set up so that the no atom is closer than 10-12 bohr
to a non-periodic boundary.
For example, in a single-layer slab calculation (all atoms at z=0),
the supercell should extend 10-12 bohr in both +z and -z,
requiring a supercell of total length 20-24 bohr in the z-direction.
In a multi-layer slab calculation, with atoms ranging from z=-4 (bohr)
to z=+4, the supercell needs to stretch from [-14,14] or
a total of 28 bohr.
Important: the coordinate origin for the atomic input is,
by default, positioned at the center of the supercell (strictly speaking,
this is for non-periodic directions only). For example, in the slab
calculation mentioned above, if the atom positions ranged from z=0
to z=+10, one would need a supercell that ranged from z=-10
to z=+20 to contain the density, a width of 30 bohr.
However, with z=0 defined as the center of the supercell, one would
need a supercell to stretch from z=-20 to z=+20,
a width of 40 bohr.
The supercell origin would need to be shifted to center the slab in the
supercell to be able to take advantage of using the smaller supercell.
Choice of the dimensions of the grid is guided by a compromise
of two considerations. Greater accuracy in the numerical
quadratures requires larger grid dimensions (more grid points),
but more grid points means a more expensive (in both memory and cpu)
calculation. Experience has indicated that most calculations are
converged (assuming orthogonal vectors) with a grid interval of
0.30-0.35 bohr along each of the lattice vectors. With a cubic
30.0x30.0x30.0 box, for example, grid dimensions of 100x100x100 would
normally be well converged.
For faster calculations where cruder accuracy is sufficient, a spacing
of 0.4-0.5 bohr can work.
For very fine accuracy, and for problems containing bad actors like
oxygen, a very "hard" atom, a finer grid might be necessary to improve
the energy calculation or improve the accuracy of a force calculation
(for a geometry calculation).
In that event, grids with spacings as small as 0.25 or even 0.20 can be
useful.
SeqQuest uses the "Local Moment CounterCharge" (LMCC) method for
correcting the supercell electrostatics. For systems with a vacuum
gap (molecules, or slabs), SeqQuest automatically applies a "vacuum LMCC":
In a periodic slab (ndim=2) with a planar (normal) dipole,
or a molecule/cluster (ndim=0) calculation with a net charge or dipole,
the LMCC is invoked automatically (without any input on the part of the
user), and supercell effects up to a dipole are treated exactly.
Supercell errors from quadrupole and higher moments are not removed,
but those errors scale as L-5 or smaller, where L is the
linear dimension of the supercell.
Use of SeqQuest on molecules with a net charge or dipole, or a polar
slab calculation (with a planar dipole) should cite the first paper above.
For a charged (local) defect in a periodic system (e.g.,
a +1 state for the nitrogen substitutional defect in bulk silicon),
the situation is more complicated because of the need to make
workable boundary conditions. The defect-LMCC method is then called
for, but its use is very involved, and should be done only by those
who are expert in the use of SeqQuest and only after detailed
consultations. This is a very new, and not completely researched
method for treating boundary conditions for defects. Anyone attempting
to use this method for a charged bulk defect should read and understand,
in detail, the defect-LMCC paper. The keyword "ionopt" tells the code
which method to use. If the defect-LMCC method is invoked (ionopt=-2)
for a charged defect, then a presumptive location for the charge must
be specified (using the "rchrg " keyword) so that the code knows where
to locate its LMCC. In addition, to extract useful total energies,
an energy reference (i.e., electron chemical potential) must be
established. There are multiple options a user has to try and do
this, and all are confusing and error-prone. Any calculation of
charged defects should be considered highly "researchy".
WARNINGS about the LMCC:
For periodic calculations (ndim=1,2,3),
a BZ sample is required, and the kgridZ keywords need to be invoked.
SeqQuest has only a very primitive scheme for building a BZ sample.
In the following discussion, we assume 3D bulk (ndim=3), but the
1D and 2D cases are handled analogously. Taking {A,B,C} as
the primitive lattice (supercell) vectors, we get the reciprocal
lattice vectors GA in the usual way.
The code then generates a regular grid in the parallelpiped defined by
the reprical lattice vectors: GA/n_grid_A, etc.
SeqQuest, by default, shifts this BZ grid off of the gamma-point
to the body-centered location (i.e., the "kgrid " keyword).
This offset is usually a more efficient (convergent) k-sample for a given
number of points than centering a k-grid at the gamma point.
For an orthorhombic cell (e.g. cubic) this is true,
but for a hexagonal cell, the resulting k-grid does not have the needed
symmetries about the body-center point in the grid.
The offset k-sample in the hexagonal plane is anisotropic, introducing
an artificial symmetry-breaking to the system.
To make the sampling symmetric for a hexagonal system (hexagonal in
the x-y plane!), we must use either
"kgrid2" or "kgridh" so that the k-grid is not shifted off
gamma in the x-y plane, and is shifted only in the z-direction.
Use of "kgrid3" uses a gamma-centered grid, i.e., without any shift.
SeqQuest automatically uses any symmetry specified in the input
to reduce the generated BZ sample to k-points in the irreducible BZ.
To get a gamma point sample for a periodic calculation, enter
"0 0 0" as input to the "kgrid " keyword. The "0" input
causes a single interval along that reciprocal lattice vector,
with the k-point coordinate at gamma in that direction.
For a 2D (ndim=2) calculation, n_kgrid_C must be zero (i.e. gamma
point in the non-periodic z-direction).
For a 1D calculation, both n_kgrid_C and n_kgrid_B
must be entered as zero.
For bulk defect calculations (and closed-shell molecular calculations),
a "discrete defect occupation" (DDO) scheme is available to replace the
conventional fermi-dirac method for occupying states. DDO enforces
closed shell (T=0K) occupancies, and, in bulk, prevents metallic
occupations. See PRL 96, 246401 (2006). The DDO scheme is invoked
by using the closed option in the
Run phase Section of the input file.
of the Ceperley/Alder electron gas results
The default GGA is PBE
Also available are PW91,
BLYP, using Becke exchange
with Lee/Yang/Parr correlation
and AM05:
Return to TopDimension of system
SeqQuest is capable of calculations of finite molecule/cluster (ndim=0),
as well as periodic 1D chain (ndim=1), 2D slab (ndim=2), and bulk 3D (ndim=3)
calculations. Note that a molecule/cluster (ndim=0) calculation of a
Na-Cl molecule, for example, is formally different than a bulk molecular
crystal (ndim=3) calculation of Na-Cl, even if one uses the same primitive
lattice vectors!
The choice of dimension has implications throughout the input and calculation:
Important: The code has very definite ideas about which
directions are periodic and which go off to vacuum in chain and slab
calculations (the point is moot in molecular or bulk calculations).
For a slab (ndim=2) calculation, the periodic directions must be in
the x-y plane and the third, non-periodic, lattice vector
must be along the z-axis.
For 1D chain (ndim=1) calculation, the periodic directions must be along
the x-axis, and the non-periodic lattice vectors must be
normal to the x-axis, i.e., must be in the y-z plane.
Return to Top Scale factors
The purpose of the scaling factors is to easily modify the length
dimensions without having to edit every single coordinate (lattice vectors,
atomic position vectors, k-points) in the input file. The scaling functions
act to scale every common coordinate in the problem. The "scale" keyword
scales everything, the scalex/scaley/scalez keywords scale the individual
coordinates (which can aid in such things as altering the c/a ratio for
a crystal input), and the "scaleu" function scales the periodic directions
only (e.g. the x-y coordinates for an ndim=2 slab calculation).
Return to Top Lattice vectors
The code is a supercell code, and the primitive lattice vectors define
the supercell. Hence, even when doing a ndim=0 molecular calculation,
all three primitive lattice vectors must be specified.
Return to Top Grid dimensions
The regular space (fft) grid on which many of integrals in Quest are
performed is defined by primitive grid vectors: the primitive lattice
vectors divided by the respective grid dimensions. Hence the grid
directions are aligned with the cell directions.
Return to TopCharge state calculations and multipole moments in supercells
In a supercell code, special consideration must be given to the
treatment of supercell effects in systems that have a net charge,
or have a significant dipole or higher multipole moment.
SeqQuest corrects the Coulomb potential (not just the energy) for the
contamination of the local potential by the artificial periodic images
introduced in the supercell approximation, reconstructing the local
potential correct for an isolated charge or dipole.
"Local electrostatic moments and periodic boundary conditions",
P.A. Schultz, Phys. Rev. B 60, 1551 (1999).
For treating a defect charge (or dipole) in a periodic system,
a "defect-LMCC":
"Charged local defects in extended systems",
P.A. Schultz, Phys. Rev. Lett. 84, 1942 (2000),
can be used. For an illustration of an application of this method
to computing defect levels in silicon, see the following:
"Theory of defect levels and the 'band gap problem' in silicon"
P.A. Schultz, Phys. Rev. Lett. 96, 246401 (2006).
Return to TopBrillouin Zone (k-point) sampling
Brillouin Zone (BZ), or k-point, sampling is a necessary burden of
periodic calculations.
For molecular calculations (ndim=0), BZ sampling is moot, as assumed
to be the gamma point.
Return to TopSymmetry
Symmetry in Quest is used to:
The code does not deduce the symmetry of the system, nor does it
know anything about space/point groups; the desired symmetries
must be specified in the input file by the user.
The user need not specify all the symmetry operations for a given
symmetry group in the input file, just those that are sufficient
to define a group (i.e., a minimum basis that expands to a group).
The code will automatically expand the entered elements into the full group.
The symmetry operations have a general input: a type of symmetry
(expressed as a rotation with a possible inversion) around a
symmetry axis, with a possible translation (to allow for
non-symorphic groups):
This convention allows for a very natural (and very compact) scheme
for describing any general point group or space group. For example,
the bulk cubic symmetry, a group with 48 total symmetry operations,
can be described with four input symmetry definitions:
a 4-fold rotation about the z-axis,
a 3-fold rotation about the 111-axis,
a 2-fold rotation about the 110-axis,
and an inversion:
|i_symtype | = order of rotation (2-fold,3-fold, etc)
i_symtype < 0 = rotation plus inversion
i_symtype = -1 is simple inversion
i_symtype = 1 or -2 is a reflection (2-fold+inversion=reflection)
Axis need not be normalized, but must be non-zero (except for inversion)
symops - for cubic symmetry
4
definitions of symmetry operations
4 0.0 0.0 1.0 0.0 0.0 0.0
3 1.0 1.0 1.0 0.0 0.0 0.0
2 1.0 1.0 0.0 0.0 0.0 0.0
-1 0.0 0.0 0.0 0.0 0.0 0.0
These four symmetry operations are sufficient to define the group; SeqQuest
will internally expand these four input elements to generate the full group
of 48 symmetry elements.
Note that the inversion has a zero length axis. This is a special case, as
axes for all other symmetry types must be non-zero. The cubic group needs
no translations (note translation vectors are all zero) in its definitions,
but other (non-symorphic) symmetry groups will have translation.
To see examples of how to define the symmetries for a variety of different
crystal symmetries,
see symmetry input examples.
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Send questions and comments to:
Peter Schultz
at
paschul@sandia.gov
Last updated: December 2, 2010