ACCURACY • ATOMS • ATOMTYPE • BASIS • COMMENT • CONVERGENCE • COORDINATES • DEFINE • DIIS • DOS • FORMFACTORS • FRAGMENTS • FRAGMENTLABELS • GROSSPOPULATIONS • IGNORE • KLABELS • KSPACE • LATTICE • MAXMEMORYUSAGE • NATOMSASFRAGMENT • ORBITALLABELS • ORBITALPLOT • OVERLAPPOPULATIONS • PLANEWAVES • PRINT • RELATIVISTIC • RESPONSE • RESTART • SCF • STOPAFTER • TAILS • TITLE • UNITS • UNRESTRICTED • XC
General precision parameter. Default value = 3.5. High values
(larger than 4.5 say) should only be used in extreme cases. Values below 3.0
produce unreliable results, due to the limited precision in integrals.
Accuracy plays in fact the role of a very general accuracy parameter.
It determines not only the generation of integration points
(it is the default of the AccInt key for the integration scheme),
but also the (default) values of many other
parameters and settings that are related to the accuracy of the results.
Nuclear coordinates. The chemical symbol (H, C, Cu, etc.), which defines the atom type, must be given on the keyword-line. The data-records contain the coordinates, one atom per line. The coordinates are in cartesian representation unless the key Coordinates has been given in input with the value natural, in which case the numbers are interpreted as expansion coefficients in the Bravais lattice vectors (see key Lattice). In case of the cartesian representation the values are in atomic units (angstroms if the unit of length has been changed with key Units). The atoms key must occur once for every atom type, i.e. the number of atom types is defined as the number of occurrences of this key.
Description of the atom type. Contains the block keys Dirac, BasisFunctions and FitFunctions. The key corresponds to one atom type. The ordering of the AtomType keys (in case of more than one atom type) is not arbitrary. It is interpreted as corresponding to the ordering of the Atoms keys. The n-th AtomType key supplies information for the numerical atom of the nth type, which in turn has atoms at positions defined by the nth Atoms key.
ATOMTYPE Symbol
DIRAC ChemSym
{option}
...
shells cores
shell_specification {occupation_number}
...
SUBEND
{BASISFUNCTIONS
shell_specification STO_exponent
...
SUBEND}
FITFUNCTIONS
shell_specification STO_exponent
...
SUBEND
END
The argument Symbol to AtomType is the symbol that is used in the Atoms key block.
Specification of the numerical ('Herman-Skillman') free atom,
which defines the initial guess for the SCF density, and which also
(optionally) supplies Numerical Atomic Orbitals (NOs) as basis functions, and/or as fit functions for the
crystal calculation. The argument ChemSym
of this option is the chemical symbol of the atom type.
The data records of the Dirac key are:
1.the number of atomic shells (1s,2s,2p,etc.) and the nr. of core-shells (two integers on one line). 2,3
specification of the shell and its electronic occupation.
This specification can be done via quantum numbers or using the standard designation (e.g. '1 0'
is equivalent to '1s').
Optionally one may insert anywhere in the Dirac block a record
Valence,
which signifies that all numerical valence orbitals will be used as basis functions (NOs) in the crystal
calculation.
You can also insert NumericalFit
followed by a number (max. l-value) in the key block, which causes the program to use numerical fit functions.
For example NumericalFit 2 means that the squares of all
s,p, and d NOs will be used as fit functions with l=0, since the NOs are
spherically symmetric.
If you insert Spinor,
a spin-orbit relativistic calculation for the single-atom will be carried out.
The Herman-Skillman program generates all its functions (atomic potential, charge density, one-electron states) as tables of values in a logarithmic radial grid. The number of points in the grid, and the min. and max. r-value are defaulted at 3000, 0.000001, and 100.0 (a.u.) respectively. These defaults can be overwritten by specifying anywhere in the dirac block the (sub)keys radial, rmin and rmax.
The program will do a spin-unrestricted calculation for the atoms in addition to the restricted one. The occupation of the spin-orbitals will be of maximum spin-multiplicity and cannot be controlled in the DIRAC key-block.
Slater-type orbitals, specified by quantum numbers n,l or by the letter designation (e.g. 2p) and one real (alpha) per sto. One sto per record. Use of this key is optional in the sense that Slater-type functions are not needed if other basis functions have been specified (In the first place: numerical atomic orbitals, see key DIRAC. In the second place (only in bulk crystals): plane waves, see the key planewaves)
Slater-type fit functions, described in the same way as in basisfunctions.
Each fitfunctions key corresponds to one atom type,
the type being the one of the preceding DIRAC key.
The selection choice of a 'good' fit set is a matter of experience.
Fair quality sets are included in the database of the molecular program adf.
Example:
ATOMTYPE C :: Carbon atom
DIRAC C
3 1
VALENCE
1s
2s
2p 2.0
SUBEND
BasisFunctions
1s 1.7
...
SubEnd
FitFunctions
1s 13.5
2s 11.0
...
SubEnd
END
Remarks
Other subkeys of the AtomType
key block are CoreFunctions
and TestFunctions
that have the same format as the BasisFunctions
and FitFunctions
blocks. The TestFunctions
block specifies STOs to be used as test functions in the numerical integration package.
The CoreFunctions key specifies the
use of Slater type auxiliary functions to enforce that valence basis functions are orthogonal to all
core orbitals. By default this is achieved by explicitly (numerically)
projecting out the component of the core orbitals from the valence functions.
This key is currently disabled.
Block key containing options and thresholds related to the basis set. See also second list.
Needed to make a fragment (input) file.
Fragment option that uses molecular fragments. The basis is actually transformed to the fragment basis. Keys Fragments and NatomsAsFragment are required.
The content of this key is a text that will be copied to the output header, where general program information is also printed.
All options and parameters related to the convergence behavior of the SCF are defined in this block key. Also the finite temperature distribution is part of this. See also second list.
Criterion for termination of the SCF procedure. Default depends on Accuracy, for instance 3e-4 for Accuracy 4.0
Requires a numerical argument, which is an energy width, in a.u.. It simulates a finite-temperature electronic distribution. By default, zero temperature is assumed. The key may be used to achieve convergence in an otherwise problematically converging system (slabs, typically). The energy of a finite-T distribution is different from the T=0 value, but for small T a fair approximation of the zero-T energy is obtained by extrapolation. The extrapolation energy correction term is printed with the survey of the bonding energy in the output file. Check that this value is not too large. Build experience yourself how different settings may affect the outcomes. Remember that this key is meant to help you overcome convergence problems, not to do finite-T research: only the electronic distribution is computed T-dependent, other aspects are not accounted for!
Smooths (slightly) occupation numbers around the Fermi level, so as to insure that nearly-degenerate states get (nearly-) identical occupations. Default=off, but in case of problematic SCF convergence the program will turn this key on automatically, unless the key Nodegenerate is set in input. The smoothing depends on the argument to this key, which can be considered a 'degeneration width'. When the argument reads 'default', the program will use a default value for the energy width (1e-4).
The only sensible value for this key is: natural, which specifies that nuclear coordinates (key atoms) are given as expansions in the Bravais lattice vectors, rather than in a Cartesian representation.
Definition of user-supplied functions and variables that can subsequently be used in the input file. (see the note on auxiliary input features)
Most interesting option is DiMix. See second list.
General Density-Of-States information.
DOS
{ File filename }
{ Energies n }
{ Min emin }
{ Max emax }
End
Where n is the number of
(equidistant) energy-values, emin, emax the minimum and
maximum energy values (with respect to the Fermi energy), and filename the (formatted) file on which
the DOS-information will be written. If the file is omitted, the information
will be printed in the output file.
Example:
DOS
FILE plotfile
ENERGIES 500
MIN -.35
MAX 1.05
END
According to this example, density-of-states values will be
generated in an equidistant mesh of 500 energy values, ranging from 0.35 below
the Fermi level to 1.05 above it (atomic units). All information will be
written to a file plotfile. The
information on the plot file is a long list of pairs of values (energy and DOS), with some informative text-headers and general information; since the file is
formatted one can easily inspect its contents; it should be suitable for
graphical software like IGOR.
Density-of-states values are generated for the total D.O.S. and optionally also for some partial densities of
states (see the keys GrossPopulations
and OverlapPopulations).
If the key DOS is omitted,
no Density-of-States information is generated at all.
If the key is given, but one or more of the 'subkeys' (file, energies, min, max) are omitted, default values
are inserted (: direct printing on output, 300, -0.75, 0.75).
X-ray structure factors (Fourier analysis of the charge density) are computed after termination of the SCF procedure; the key should be followed by an integer specifying the number of stars of K-vectors for which the structure factors are computed. Default (omission of the key): 3 stars.
Define fragments. This key takes as argument the fragment file name (absolute path or path relative to the executing directory) and its contents are for each atom in the fragment two integers: atom number in the fragment versus atom number in this calculation.
The program will generate labels for the fragment orbitals
automatically by default. With this option you can assign your own label to
each fragment orbital.
Example:
FRAGMENTLABELS
Sigma
Sigma*
Pi_x
Pi_y
Pi_x*
Pi_y*
End
In this example the first four fragment orbitals will be labeled
as stated in the body of this key. The remaining orbitals are labeled by the
default labeling system (e.g. 1/FO/5, etc.). The labels are used in combination
with options like PRINT EIGENS and PRINT ORBPOP. (See also PRINT ORBLABELS).
This key can be given once for each fragment.
Partial densities-of-states are generated for the gross populations listed under this key.
GROSSPOPULATIONS
{ iat lq }
{ FragFun jat ifun }
{ Frag kat }
{ Sum
...
EndSum }
End
Each line contains a PDOS instruction.
There are three possibilities:
1 Line contains two integers, the first specifying the atom (iat)
(numbered according to the total list comprised from all atoms-keys),
the second the l-value (lq) (0:s, 1:p, 2:d, and so on).
Partial densities of states are generated for all real
spherical harmonics belonging to the specified l-value.
2 Line is of the form: Frag kat,
which means that the PDOS
of the functions belonging to atom kat will be calculated.
3 Line is of the form fragfun jat ifun,
which refers to the function ifun of atom jat,
including core states of that atom.
You can sum PDOS commands with a sum-block,
i.e. specify any number of any of the three PDOS
specifications in a block that starts with Sum
and ends with EndSum.
Example:
GROSSPOPULATIONS
FRAGFUN 1 2:: Second function of first atom
FRAG 2 :: Sum of all functions from second atom
SUM:: sum following PDOSes
FRAG 1::Atom nr.1
FRAGFUN 2 1::First function of second atom
5 1:: All p functions of fifth atom
ENDSSUM
END
Suppress reading of input until the next end-key code (END).
With this key you assign names to symmetry unique k-points. In general you do not know in advance how many k-points will be used, nor the number of points that are symmetry unique among them. Therefore you should first add to your input file the option StopAfter gemtry, which causes the program to stop after the k-points have been generated. In the output you will see under the header k-space integration a numbered list of the k-points, with their, symmetry-unique-index number, and coordinates. In the next run you may then give the symmetry unique k-points symbolic names.
Example:
KLABELS
GAMMA
X
M
END
According to this example all k-points with symmetry unique number 1, will be labeled gamma, those with symmetry unique number 2 X, and those with symmetry unique number 3 M.
Parameter for numerical integration over the Brillouin Zone (k-space).
An integer value should be supplied. 1=absolutely minimal (only the G-point is used),
2=linear tetrahedron method, coarsest possible spacing, 3=quadratic tetrahedron method, coarsest
spacing. Higher values should be chosen odd (5, 7,..) to use the quadratic method; even values (4,6,..)
trigger the linear tetrahedron method, which is usually by far inferior.
cpu-time increases very rapidly with higher kspace-values:
try 3 for a reasonable result, or 5 for higher precision.
The key may occur as a block key, the contents of the key are options that handle in more detail the integration of
the Brillouin zone.
E.g. the subkey Kinteg
takes over the simple key Kspace.
For other settings, see the explanation of Kspace
in the second list.
Default depends on Accuracy, the integration parameter in real space.
Vectors defining the Bravais lattice, one vector per line. The number of lines defines the periodicity of the system: 1: polymer, 2: slab, 3:bulk crystal. Each vector has three coordinates (Cartesian), in atomic. To specify coordinates in Angstrom, use the Units key.
The maximum amount of memory which may be allocated by workspace manager of the program, in Megabytes. Note that the program needs more memory than you specify here, e.g. due to the use of Fortan 90 allocates and I/O buffering.
This key is followed by a number n, signifying that the first n atoms are to be treated as a fragment. Your input file must contain the fragments blocks. You can have more than one fragment, in which case this key should be followed by a series of numbers, n1 n2..., which means that the first fragment consists of the first n1 atoms, the second fragment of the n2 next atoms, etc. Now the file should contain the fragments blocks of the first fragment, followed by the fragments blocks of the second fragment...
The program will generate labels for the valence basis states
automatically by default. With this option you can assign your own label to
each valence function.
Example:
ORBITALLABELS
SIGMA
2P_Y
2P_Z
2P_X
END
In this example there are four valence basis functions. The first
will be labeled SIGMA, the second 2P_Y and so on.
The labels are used in combination with options like print eigens
and print orbpop.
(See also print orbitallabels).
Description of the automatic labels for the valence basis. This basis contains
core functions needed for orthogonalization on the core. A normal atomic basis
function, i.e. a numerical orbital or a Slater type orbital, gets a label like
<atom number>/<element>/<orbital type>/<quantum numbers
description>/<exp in sto>
Example with a Li and a H atom:
1/LI/NO/1s
1/LI/NO/2s
1/LI/STO/2s/1.4
1/LI/STO/2p_y/1.3
1/LI/STO/2p_z/1.3
1/LI/STO/2p_x/1.3
2/H/NO/1s
2/H/STO/1s/1.9
...
Core states and plane waves will just get simple numbers as labels:
CORE STATE 1
CORE STATE 2
PW1
PW2
Currently disabled.
With a result file of a previous calculation you may rerun the program,
using that file for restart,
to make a plot file of the real part of the eigenvectors in a plane.
Only eigenstates are treated that belong to bands which fall (at least
partially) in the energy range defined by the DOS key.
Therefore, the orbitalplot
key must be used in conjunction with the DOS key.
The first four records in this key-block describe the set of plot points.
The first record is the starting point (three coordinates). The second record
should contain a vector, relative to the starting point, and a step size. The
same holds for the third record. The plot points are generated in a plane
spanned by these two vectors. The fourth record determines the amount of steps
that are taken in the two directions. A plot point must not coincide with the
position of an atom, because that would give rise to a singularity in the
potential evaluation. If this happens, you have to displace the starting point.
You control which eigenvectors are used by a next series of records. Each such
record contains the index of a k-point in the list of all symmetry unique
k-points, and two integers that specify the range of bands to be used.
Example:
ORBITALPLOT :: Make plot file of eigenvectors
0. 0. 0. :: Starting point
1. 0. 0. .1 :: Vector1 and step1
0. 1. 0. .1 :: Vector2 and step2
10 10 :: N1 and n2
2 1 5 :: Make plots for k=2 from band 1 to 5
4 1 1 :: Make plot for k=4 and band =1
...
...
END
The resulting 'plot data' are printed in the standard output file, in the format:
x y value.
X and y are relative coordinates in the selected plane, with the
origin defined as the lower-left corner, and value is the orbital value. All
data for a particular orbital are contiguous, followed by the data for the next
orbital, et cetera.
You can make a plot file of the basis functions, instead of
eigenvectors, by inserting the option:
plotprimitive into the key-block header.
Example:
ORBPLOT PLOTPRIMITIVE :: Make plot file of basis functions
......
END
OVERLAPPOPULATIONS (block-type)
Overlap population weighted densities-of-states are generated for the overlap populations listed
OVERLAPPOPULATIONS
Left
{ iat lq }
{ FragFun jat ifun }
{ Frag kat }
Right
...
End
You can use this to get the overlap population weighted
densities-of-states (OPWDOS),
also known as the crystal orbital overlap population (COOP),
of two functions, or, if you like, one bunch of functions
with another bunch of functions.
The key-block should consist of left-right pairs.
After a line with left you enter lines that specify one or more
functions (see GrossPopulations),
followed by a similar structure beginning with right,
which will produce the OPWDOS of the left functions with the right functions.
Example:
OVERLAPPOPULATIONS
LEFT::First OPWDOS
FRAG 1
RIGHT
FRAG 2
LEFT:: Next OPWDOS
FRAGFUN 1 1
RIGHT
2 1
FRAGFUN 3 5
END
warning: currently disabled!
The integer after this key specifies the number of stars of K-vectors,
defining plane wave basis functions that will be used in the crystal valence
basis. Can be used only in bulk crystals. Default: no plane waves at all, only
Atomic Orbitals (numerical from the Herman-Skillman program, and Slater-type,
via the subkey Basisfunctions of key AtomType)..
One or more strings (separated by blanks or comma's) from a pre-defined set may be typed after the key. This induces printing of various kinds of information, usually only used for debugging and checking. The set of recognized strings frequently changes (mainly expands) in the course of software-developments. Useful arguments may be symmetry, and fit. A list of all important arguments to this key follows:
Prints the (complex) coefficients in the form (norm, phase factor) of the eigenvectors with respect to the valence basis. Coefficients with a norm smaller than eigthreshold will be skipped. This threshold can be set with the option eigthreshold x, default x=.01.
Prints in the output the eigenvectors in the gamma point.
Print the estimate of the memory usage taken into account to determine the block size and the number of K points treated together.
Prints overlap population of all basis functions.
Prints the labels of the orbitals. If you are interested in the labels of an old calculation and you don't want to repeat it completely, you can add the option StopAfter gemtry to your input file.
Prints the Mulliken population per orbital, for all eigenstates. This is the most detailed population analysis that you can get, one for all k-points and for each band. Populations below a certain threshold are ignored. This threshold can be set with the option popthreshold x. By default x =.01.
Print the information about the distance effects used in the numerical integrals.
Includes a relativistic correction in the Hamiltonian. This key replaces the keys ZORA and SRZORA of the previous versions of ADF-BAND.
RELATIVISTIC {level} {formalism} {potential}
Level
May be NONE (no relativistic effects), Scalar (default) or SpinOrbit.
Formalism
Only ZORA is supported (no Pauli)
Potential
Only frozen is supported (no full)
Perform a time-dependent DFT calculation to obtain real and imaginary parts of frequency-dependent dielectric function.
RESPONSE
nfreq 5
strtfr 0.0
endfr 0.01
cnvi 0.001
cnvj 0.001
ebndtl 0.001
ifxc 0
isz 0
iyxc 0
END
Omitting the specific options in the RESPONSE block will cause default setting to be used during the calculation, as given above.
nfreq the number of frequencies in a.u. for which a TDDFT calculation is performed when calculating the dielectric function εe(ω) of a system (default=5).
strtfr is the start frequency in a.u. of the frequency range over which the dielectric function is calculated (default=0d0).
endfr is the end frequency in a.u. of the frequency range over which the dielectric function is calculated (default=1d-2).
cnvi the first convergence criterion for the change in the fitcoefficients for the fitfunctions, when fitting the density (default=1d-3).
cnvj the second convergence criterion for the change in the fitcoefficients for the fitfunctions, when fitting the density (default=1d-3).
ebndtl the energy band tolerance, for determination which routines to use for calculating the numerical integration weights, when the energy band posses no or to less dispersion (default=1d-3).
ifxc integer indicating which fxc kernel is used (default=0).
0 = Adiabatic Local Density Approximation (ALDA) (Can. J. Phys. 58, 1200 (1985)).
1 = Gross-Kohn, frequency dependent fxc kernel (PRL 55, 2850 (1985), 57, 923 (1986)),
2 = van Leeuwen-Baerends (LB94) (PRA 49, 2421 (1994)),
Only the default option for ifxc is implemented at the moment.
isz integer indicating whether or not scalar zeroth order relativistic effects are
included in the TDDFT calculation (default=0).
0 = relativistic effects are not included,
1 = relativistic effects are included.
iyxc integer for printing yxc-tensor (default=0) (JCP 115, 1995 (2001)).
0 = not printed,
1 = printed
Tells the program that it should restart with the restart file.
RESTART filename {&
option
END}
where filename is the name of the restart file and option is the program part to do a restart for (SCF, DOS, OrbitalPlot). In its simple form the calculation will do a restart of the SCF. The option for SCF restart is currently disabled, as is OrbitalPlot. Advantage of a restart is the possibility to skip certain (time consuming) program parts.
Contains the same data as the ADF-MOL key with the same name (except for DIIS procedure parameters). See also second list.
Initial 'damping' parameter in the SCF procedure, for the
iterative update of the potential: new potential = old potential + mix
(computed potential-old potential). Default=0.075.
Note: the program automatically adapts Mixing
during the SCF iterations, in an attempt to find the optimal
mixing value.
The maximum number of SCF iterations to be performed. If zero (default value) termination of the SCF procedure will depend only on other aspects (convergence, time-out, insufficient progress towards convergence, ...).
Specifies that the program is stopped after execution of a specified program-part (subroutine). The specified name should be one of a pre-defined list. The most relevant ones are gemtry (all geometrical aspects are checked, symmetry analysis is carried out, and numbers of (symmetry-unique) integration points in real space and in k-space are determined; this part takes only little cpu-time) and atomic (in addition to the geometry-part all radial parts of basis- and fit functions are generated, and the spherically symmetric atoms are computed and inserted in the crystal; the initial charge density is defined and integrated (check on integration-precision), and the electrostatic interaction is computed between the unrelaxed free atoms).
Ignore function tails. By default no tails are ignored. Both CPU time and disk space can be saved by using the TAILS option. This option is most effective when combined with the Confine suboption, as explained in the Examples document.
TAILS {bas crbas} (core crcore)
One real argument for keys basis and core, which should be a small value; default zero. The core criterion defaults to the bas criterion (if set). In our experience, a safe value is 1e-5. The tail criterion specifies that tails of exponentially decaying (basis) functions are ignored, in the construction of Bloch functions, beyond the point where the remaining part of the function tail (radially) integrates to less than the criterion, relative to the integral of the function from zero to infinity. This option has some refinements. The advised settings for optimal performance without significant loss of accuracy is
Tails confine=1e-2 bas=1e-5 coulomb
As you see there are two new elements ('confine' and 'coulomb'). The first (confine =) specifies that all basis functions are optimized for the tails option, by multiplying the tail of the function with a rapidly decaying function. This step affects the shape of all functions outside the radius where the relative norm of the function is smaller than 1e-2. The effects on the shape of the functions are typically very small. The second new entry (Coulomb) has the effect that the criterion becomes more strict for tight functions. For safer (but slower) calculations, specify smaller values for confine and bas, such as confine=1e-3 bas=1e-6.
The TAILS keyword works must effectively when combined with the confinement keyword, described elsewhere in this document. The confine key described here should not be confused with the confinement option for each atom type. The confine option here affects functions in the region where they become very small, independent of the distance to the nucleus. The confinement option introduces a soft cut-off for all functions of a particular atom type, at a specific distance from the nucleus.
Compulsory key. Specifies the title of this run. The title is used for identification of the result files.
Units of length and angle Geometric lengths and angles are in units defined by this key.
UNITS
{LENGTH {Angstrom | Bohr}}
{ANGLE {Degree | Radian}}
END
Angstrom and Bohr, respectively Degree and Radian, are
recognized strings. Each of the subkeys is optional, as is the key UNITS
itself. Defaults: Angstrom for lengths, and Degree for angles.
The position of this key in the input is not important. It always applies to all
input.
To avoid mistakes one should place UNITS as early as possible in input (if at
all).
In the previous versions of the ADF-BAND program, the number of independent spins could be specified by the key spin. Other keys that are related to this key are nspinstartat, nspinrefat. These keys have now all been replaced by this single Unrestrictedkey. If this key occurs (no additional data needed), a spin-unrestricted calculation will be carried out.
UNRESTRICTED {StartUp | Reference | OnlyReference}
Reference
Default the formation energy is calculated with respect to the spherically symmetric spin-restricted atoms. If you want to do an unrestricted calculation for the atoms, you may include this keyword as argument to key Unrestricted.
Startup
By default the program uses as a first guess for the density the sum of the spherically symmetric spin-restricted atoms. In case you do a spin-unrestricted calculation, you may try to use the sum of the unrestricted atoms as start-up density. Supplying Startup as argument of key Unrestricted will give you as start-up density the sum of unrestricted atoms with their net spin 'up'. In combination with a frozen core this option can lead to a locally negative valence density, in which case the program will stop and tell you not to use this option.
OnlyReference
If you want a restricted calculation with as reference the
unrestricted atoms, specify this argument to key Unrestricted.
Defaults and special cases
A calculation is default restricted.
General remarks
Be aware that cpu-time and disk space requirements are approximately doubled!
Specifies the exchange-correlation.
In release 1999.x and before it was a simple key (to specify only the LDA part
of the XC functional). With release 2000 it has become a block type key with
the same format as in the molecular ADF code:
The Density Functional, also called the exchange-and-correlation (XC) functional,
consists of an LDA and a GGA part. LDA stands
for the Local Density Approximation, which implies that the XC functional in
each point in space depends only on the (spin) density in that same point. GGA
stands for Generalized Gradient Approximation and
is an addition to the LDA part, by including terms that depend on derivatives
of the density. For both terms ADF supports a large number of the formulas advocated
in the literature.
In principle you may specify different functionals to be used for the potential, which determines the
self-consistent charge density, and for the energy
expression that is used to evaluate the (XC part of the) energy of the charge
density. To be consistent, one should generally apply the same functional to
evaluate the potential and energy respectively. Two reasons, however, may lead
one to do otherwise:
1. The evaluation of the GGA part in the potential
is rather time-consuming. The effect of the GGA term in the potential on the
self-consistent charge density is often not very large. From the point of view
of computational efficiency it may, therefore, be attractive to solve the SCF
equations at the LDA level (i.e. not including GGA terms in the potential), and
to apply the full expression, including GGA terms, to the energy evaluation a posteriori: post-SCF.
2. A particular XC functional may have only an implementation for the
potential, but not for the energy (or vice versa). This is a rather special
case, intended primarily for fundamental research of Density Functional
Theory, rather than for run-of-the-mill production runs.
The key that controls the Density Functional is xc,
with sub keys LDA
and GGA (or equivalently: gradients) to define the LDA and
GGA parts of the functional. Either subkey is optional (need not be used) and
may occur twice in the data block: if one wants to specify different
functionals for potential and energy evaluations respectively, see above.
XC
{LDA {Apply} LDA {Stoll}}
{GGA {Apply} GGA}
END
Apply
States whether the functional defined on
the pertaining line will be used self-consistently (in the SCF-potential), or
only post-SCF, i.e. to evaluate the XC energy corresponding to the charge density.
The value of apply must be SCF, Energy or Always.
A value postSCF will also be accepted
and is equivalent to Energy.
A value Potential will also be
accepted and is equivalent to SCF.
For each record separately the default (if no
Apply value is given in that record) is
SCF.
For each of the two terms (LDA, GGA) in the functional:
if no record with Energy specification is found in the data block,
the evaluation of the XC energy will use the same functional as is
applied for the potential. If a GGA (Generalized Gradient Approximation) is
used in the density functional, applying it is by default suppressed in the
early stages of the SCF
procedure, to save CPU time (the
evaluation of GGA potentials may be rather time consuming).
Using Always cancels this feature so that any GGA is evaluated at every cycle of the SCF,
including the initial ones.
Defines the LDA part of the XC functional and can be any of the following:
Xonly: The pure-exchange electron gas formula. Technically this is identical to the Xalpha form (see next) with a value 2/3 for the X-alpha parameter.
Xalpha: the scaled (parameterized) exchange-only formula. When this option is used you may (optionally) specify the X-alpha parameter by typing a numerical value after the string Xalpha (separated by a blank). If omitted this parameter takes the default value 0.7
VWN: the parameterization of electron gas data given by Vosko, Wilk and Nusair (ref [1], formula version V). Among the available LDA options this is the more advanced one, including correlation effects to a fair extent.
For the VWN or GL variety of the LDA form you may include Stoll's correction [2] by typing Stoll on the same line, after the main LDA specification. You must not use Stoll's correction in combination with the Xonly or the Xalpha form for the Local Density functional.
Specifies the GGA part of the XC Functional, in earlier times often called the 'non-local' correction to the LDA part of the density functional. It uses derivatives (gradients) of the charge density. Separate choices can be made for the GGA exchange correction and the GGA correlation correction respectively. Both specifications must be typed (if at all) on the same line, after the GGA subkey.
For the exchange part the options are:
Becke: the gradient correction proposed in 1988 by Becke [3].
PW86x: the correction advocated in 1986 by Perdew-Wang [4].
PW91x: the exchange correction proposed in 1991 by Perdew-Wang [5].
For the correlation part the options are:
Perdew: the correlation term presented in 1986 by Perdew [6].
PW91c: the correlation correction of Perdew-Wang (1991), see [5].
LYP: the Lee-Yang-Parr 1988 correlation correction, [7-9]
Some GGA options define the exchange and correlation parts in one stroke. These are:
PW91: this is equivalent to pw91x + pw91c together.
Blyp: this is equivalent to Becke (exchange) + LYP (correlation).
LB94: this refers to the XC functional of Van Leeuwen and Baerends [10]. There are no separate entries for the Exchange and Correlation parts respectively of LB94
The XC energies of exchange potential EV93x (due to Engel and Vosko in 1993) and various forms of the Perdew, Burke, Ernzerhof functional (correlation and three forms of exchange) are printed.
The string GGA must contain not more than one of the exchange options and not more than one of the correlation options. If options are applied for both they must be separated by a blank or a comma.
Defaults and special cases
General remarks
