Basis set
*********

Band represents the single-determinant electronic wave functions as a
linear combinations of atom-centered basis functions (the basis set).
See also: Wikipedia page on Basis Sets.

The basis sets in Band consists of **NAOs** (Numerical Atomic
Orbitals, obtained by solving numerically the Kohn-Sham equations for
the isolated spherical atoms) augmented by a set of **STOs** (Slater
Type Orbitals).

The choice of basis set is very important, as it influences heavily
the accuracy, the CPU time and the memory usage of the calculation.
Band comes with 6 predefined types of basis sets: **SZ**, **DZ**,
**DZP**, **TZP**, **TZ2P**, **QZ4P** (SZ:  Single Zeta, DZ: Double
Zeta, DZP: Double Zeta + Polarization, TZP: Triple Zeta +
Polarization, TZ2P: Triple Zeta + Double Polarization, QZ4P: Quadruple
Zeta + Quadruple Polarization). See the sections Which basis set
should I use? and Available Basis Sets for more details.

To speed up the calculation, Band can use the **frozen core
approximation** in which core orbitals are kept frozen during the SCF
procedure (and the valence orbitals are orthogonalized against the
frozen orbitals). One can run an **all electron** calculation by
specifying "Core None" in the Basis input block. Note: some features,
such as Hybrid functionals, are incompatible with the frozen-core
approximation, and require an all electron (i.e. "Core None") basis
set.


Basis input block
=================

You can specify which basis set to use in the "Basis" input block.

   Basis
      Type [SZ | DZ | DZP | TZP | TZ2P | QZ4P | STO/TZ2P | STO/SZ | STO/DZ | STO/DZP | STO/QZ4P | 
            CORR/QZ6P | CORR/TZ3P | GTO/CC-PV5Z | GTO/DEF2-QZVPPD | GTO/CC-PV6Z | GTO/CC-PVQZ | 
            GTO/CC-PVTZ | GTO/CC-PVDZ | GTO/DEF2-SVP | GTO/DEF2-TZVP | GTO/DEF2-TZVPP | GTO/DEF2-QZVP | 
            GTO/AUG-CC-PVDZ | GTO/AUG-CC-PVTZ | GTO/AUG-CC-PVQZ | GTO/POB-TZVP]
      Core [None | Small | Medium | Large]
   End

"Basis"
   Type:
      Block

   Description:
      Definition of the basis set

   "Type"
      Type:
         Multiple Choice

      Default value:
         DZ

      Options:
         [SZ, DZ, DZP, TZP, TZ2P, QZ4P, STO/TZ2P, STO/SZ, STO/DZ,
         STO/DZP, STO/QZ4P, CORR/QZ6P, CORR/TZ3P, GTO/CC-PV5Z,
         GTO/DEF2-QZVPPD, GTO/CC-PV6Z, GTO/CC-PVQZ, GTO/CC-PVTZ, GTO
         /CC-PVDZ, GTO/DEF2-SVP, GTO/DEF2-TZVP, GTO/DEF2-TZVPP,
         GTO/DEF2-QZVP, GTO/AUG-CC-PVDZ, GTO/AUG-CC-PVTZ, GTO/AUG-CC-
         PVQZ, GTO/POB-TZVP]

      GUI name:
         Basis set

      Description:
         Select the basis set to use.                      SZ   :
         Single Z                      DZ   : Double Z
         DZP  : Double Z, 1 polarization function
         TZP : Triple Z, 1 polarization function
         TZ2P : Triple Z, 2 polarization functions
         QZ4P : Quadruple Z, 4 polarization function
         The basis set chosen will apply to all atoms in your
         structure. If a matching basis is not found a better type
         might be used.

   "Core"
      Type:
         Multiple Choice

      Default value:
         Large

      Options:
         [None, Small, Medium, Large]

      GUI name:
         Frozen core

      Description:
         Select the size of the frozen core you want to use.
         Small, Medium, and Large will be interpreted within the basis
         sets available (of the selected quality), and might refer to
         the same core in some cases.


Which basis set should I use?
=============================

The hierarchy of basis sets, from the smallest and least accurate (SZ)
to the largest and most accurate (QZ4P), is **SZ < DZ < DZP < TZP <
TZ2P < QZ4P**.

The choice of basis set is in general a trade off between accuracy and
computation time: the more accurate the basis set, the more
computationally demanding the calculation will be (both in term of CPU
time and the memory usage).

As an example, in the following table we compare accuracy v.s. CPU
time for a (24,24) carbon nanotube using different basis sets. "Energy
error" is defined as the absolute error in the formation energy per
atom using the QZ4P results as reference. [1]


Accuracy and CPU time ratio for a (24,24) carbon nanotube using different basis sets
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+-----------------------------------+-----------------------------------+-----------------------------------+
| Basis Set                         | Energy Error [eV]                 | CPU time ratio (relative to SZ)   |
|===================================|===================================|===================================|
| SZ                                | 1.8                               | 1                                 |
+-----------------------------------+-----------------------------------+-----------------------------------+
| DZ                                | 0.46                              | 1.5                               |
+-----------------------------------+-----------------------------------+-----------------------------------+
| DZP                               | 0.16                              | 2.5                               |
+-----------------------------------+-----------------------------------+-----------------------------------+
| TZP                               | 0.048                             | 3.8                               |
+-----------------------------------+-----------------------------------+-----------------------------------+
| TZ2P                              | 0.016                             | 6.1                               |
+-----------------------------------+-----------------------------------+-----------------------------------+
| QZ4P                              | reference                         | 14.3                              |
+-----------------------------------+-----------------------------------+-----------------------------------+

It is worthwhile noting that the error in formation energies are to
some extend systematic, and they partially cancel each other out when
taking energy differences. For example, if one considers the
difference in energy between two carbon nanotubes variants ((24,24)
and (24-0)) with the same number of atoms, the basis set error is
smaller than 1 milli-eV/atom already with a DZP basis set, which is
much smaller than the absolute error in the individual energies. The
same consideration holds for reactions barriers: the error in the
energy difference between different conformations is much smaller than
the error in the absolute energies themselves.

**Band gaps:**

The following figure shows the convergence WRT basis set of band gaps
(XC:PBE). While DZ is often inaccurate (since DZ lacks any
polarization function, the description of the virtual orbital space is
very poor), TZP captures the trends very well.

   [image]Convergence of Band Gaps WRT basis set for various system.
   (XC:PBE, K-Space Quality: Good)

In general, since the basis set might have different effects on
different properties, it is advisable to run a few simple calculations
to get an idea of the effect of the basis set with your property of
interest.

**A summary of the basis sets:**

* **SZ**: Single Zeta, the minimal basis set (only NAOs), serves
  mostly a technical purpose. The results are rather inaccurate, but
  it's computationally efficient. It can be useful for running a very
  quick test calculation. See also SZ-SCF-Restart.

* **DZ**: The Double Zeta basis set is computationally very efficient.
  It can be used for pre-optimization of structures (that should then
  be further optimized with a better basis set). Since it has no
  polarization functions, properties depending on the virtual orbital
  space will be rather inaccurate.

* **DZP**: Double zeta plus polarization function. Only available for
  main group elements up to Krypton. For other elements a TZP basis
  set will be used **automatically**. This is a reasonably good basis
  set for geometry optimizations of organic systems.

* **TZP**: The Triple Zeta plus Polarization basis set offers the best
  balance between performance and accuracy. This is the basis set we
  would generally recommend.

* **TZ2P**: The Triple Zeta plus Double Polarization basis set is an
  accurate basis set. It is qualitatively similar to TZP but
  quantitatively better. It should be used when a good description of
  the virtual orbital space is needed.

* **QZ4P**: Quadruple zeta plus Quadruple Polarization. This is the
  biggest basis set available. It can be used for benchmarking.


Frozen core
===========

It is recommended to use the frozen core approximation, as it is
faster, in particular for heavy elements.

In general, the frozen core approximation does not influence the
results significantly (especially if one uses a "small" frozen core).
For accurate results on certain properties (like Properties at Nuclei)
all electron basis sets are needed on the atoms of interest.

* For Meta-GGA XC functionals, it is recommended to use "small" or
  "none" frozen core (the frozen orbitals are computed using LDA and
  not the selected Meta-GGA)

* For optimizations under pressure, use "small" or "none" frozen core

**Small, Medium, and Large frozen cores:**

The possible choices for the "Basis%Core" keyword are "None", "Small",
"Medium", and "Large". How does this map to the actual Available Basis
Sets? Obviously this depends on the element. As all elements have an
all electron basis set defined, "None" maps always to this set. For
the element H there are no frozen core sets available and all options
can only lead to the all electron basis set. For elements like C there
is a single frozen core available and the three choices ("Small",
"Medium", "Large") lead to the same choice: C.1s. Most elements have
two frozen cores defined. In such a case the choices "Large" and
"Medium" point to the larger one, and "Small" to the smallest one.
With four choices "Large" maps to the largest one, "Medium" to the one
below it, and "Small" to the smallest one. This table summarizes the
logic


Mapping of the "Basis%Core" keyword to available cores (if any)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+------------------+------------------+------------------+------------------+------------------+------------------+
| #Available       | Example          | None             | Small            | Medium           | Large            |
| frozen cores     |                  |                  |                  |                  |                  |
|==================|==================|==================|==================|==================|==================|
| 0                | H                | H                | H                | H                | H                |
+------------------+------------------+------------------+------------------+------------------+------------------+
| 1                | C C.1s           | C                | C.1s             | C.1s             | C.1s             |
+------------------+------------------+------------------+------------------+------------------+------------------+
| 2                | Na Na.1s Na.2p   | Na               | Na.1s            | Na.2p            | Na.2p            |
+------------------+------------------+------------------+------------------+------------------+------------------+
| 3                | Rb Rb.3p Rb.3d   | Rb               | Rb.3p            | Rb.3d            | Rb.4p            |
|                  | Rb.4p            |                  |                  |                  |                  |
+------------------+------------------+------------------+------------------+------------------+------------------+
| 4                | Pb Pb.4d Pb.4f   | Pb               | Pb.4d            | Pb.5p            | Pb.5d            |
|                  | Pb.5p Pb.5d      |                  |                  |                  |                  |
+------------------+------------------+------------------+------------------+------------------+------------------+

It is possible to control both the basis and core per atom type and
per region, see More Basis input options.


Available Basis Sets
====================

The basis set files, containing the definition of the basis set, are
located in "$AMSHOME/atomicdata/Band".

The next table gives an indication frozen core (*fc*) standard basis
sets are available for the different elements in BAND. Note that all
electron (*ae*) basis set are available for all basis sets types.


Available standard basis sets for non-relativistic and ZORA calculations H-Ubn (Z=1-120)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+----------------------+----------------------+----------------------+----------------------+----------------------+
| Element              | frozen core          | SZ, DZ               | DZP                  | TZP, TZ2P, QZ4P      |
|======================|======================|======================|======================|======================|
| H-He (Z=1-2)         | ae                   | Yes                  | Yes                  | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Li-Ne (Z=3-10)       | ae .1s               | Yes                  | Yes                  | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Na-Mg (Z=11-12)      | ae .1s .2p           | Yes                  | Yes                  | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Al-Ar (Z=13-18)      | ae .1s .2p           | Yes                  | Yes                  | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| K-Ca (Z=19-20)       | ae .2p .3p           | Yes                  | Yes                  | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Sc-Zn (Z=21-30)      | ae .2p .3p           | Yes                  |                      | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Ga-Kr (Z=31-36)      | ae .3p .3d           | Yes                  | Yes                  | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Rb-Sr (Z=37-38)      | ae .3p .3d .4p       | Yes                  |                      | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Y-Cd (Z=39-48)       | ae .3d .4p           | Yes                  |                      | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| In-Ba (Z=49-56)      | ae .4p .4d           | Yes                  |                      | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| La-Lu (Z=57-71)      | ae .4d .5p           | Yes                  |                      | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Hf-Hg (Z=72-80)      | ae .4d .4f           | Yes                  |                      | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Tl (Z=81)            | ae .4d .4f .5p       | Yes                  |                      | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Pb-Rn (Z=82-86)      | ae .4d .4f .5p .5d   | Yes                  |                      | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Fr-Ra (Z=87-88)      | ae .5p .5d           | Yes                  |                      | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Ac-Lr (Z=89-103)     | ae .5d .6p           | Yes                  |                      | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Rf-Og (Z=104-118)    | ae .5d .5f           | Yes                  |                      | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Uue-Ubn (Z=119-120)  | ae .5f               | Yes                  |                      | Yes                  |
+----------------------+----------------------+----------------------+----------------------+----------------------+

* element name (without suffix): all electron (ae)

* .1s frozen: 1s

* .2p frozen: 1s 2s 2p

* .3p frozen: 1s 2s 2p 3s 3p

* .3d frozen: 1s 2s 2p 3s 3p 3d

* .4p frozen: 1s 2s 2p 3s 3p 3d 4s 4p

* .4d frozen: 1s 2s 2p 3s 3p 3d 4s 4p 4d

* .4f frozen: 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f

* .5p frozen: 1s 2s 2p 3s 3p 3d 4s 4p 4d 5s 5p (La-Lu)

* .5p frozen: 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p (other)

* .5d frozen: 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d

* .6p frozen: 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 6s 6p (Ac-Lr)

* .5f frozen: 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p

Note:

  Not all combinations of basis set "Type" and "Core" are available
  for all elements. If a specific combination is not available, Band
  will pick the first *better* basis set. E.g. if an element is not in
  the DZP database, it is taken from the TZP basis set.


Pure STO and GTO basis sets
===========================

Starting from AMS2023, BAND includes many basis sets to reproduce
literature data. The basis sets are suitable (and recommended) for
well converged GW, RPA, and double hybrid calculations in which
electron-electron interaction effects are accounted for explicitly
beyond DFT. Available basis sets are:

**pure STO type basis sets**

The TZ2P and QZ4P basis sets from ADF can now be used in BAND
calculations as well. To get the same results as ADF, it is
additionally necessary to disable the confinement of the basis
functions Confinement of basis functions. Additionally, the CORR/TZ3P
and the CORR/QZ6P basis sets of ADF can also be used with BAND. Band
also includes the Corr/TZ3P_G and the Corr/QZ6P_GH basis sets which
includes higher-angular momentum functions (g-functions fo TZ3P_G,
g-,h- (and sometimes i-)functions for QZ6P_GH).

   Basis Type=STO/TZ2PSTO
   SoftConfinement Quality=Excellent # disable radial basis function confinement


STO (all electron) basis sets for band
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+----------------------------------------------------+----------------------------------------------------+
| Basis Set                                          | ADF                                                |
|====================================================|====================================================|
| STO/TZ2PSTO                                        | ZORA/TZ2P                                          |
+----------------------------------------------------+----------------------------------------------------+
| STO/QZ4PSTO                                        | ZORA/QZ4P                                          |
+----------------------------------------------------+----------------------------------------------------+
| CORR/QZ6P                                          | CORR/QZ6P                                          |
+----------------------------------------------------+----------------------------------------------------+
| CORR/QZ6P_GH                                       |                                                    |
+----------------------------------------------------+----------------------------------------------------+
| CORR/TZ3P                                          | CORR/TZ3P                                          |
+----------------------------------------------------+----------------------------------------------------+
| CORR/TZ3P_G                                        |                                                    |
+----------------------------------------------------+----------------------------------------------------+

**Correlation consistent Gaussian type basis sets**

See also: Examples GTO

BAND includes the correlation-consistent (CC) Dunning Gaussian type
(GTO) basis sets from double Zeta (DZ) to hextuple Zeta (6Z) quality.
GTO basis sets can only be used in non-relativistic calculations and
can not be used with the frozen core approximation. The basis sets cc-
pVDZ to cc-pV5Z are only available for the first four rows of the
periodic table, with the exception of K (potassium) (see also: the
information on the Basis Set Exchange. The cc-pV6Z basis set is only
available for the elements of the first three rows of the periodic
table with the exception of Li, Na, and Mg.

   Basis Type=GTO/CC-PVTZ
   SoftConfinement Quality=Excellent # disable radial basis function confinement
   Relativity Level=None   # relativistic effects are currently not supported for GTOs


GTO (all electron) basis sets for band
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+----------------------------------------------------+----------------------------------------------------+
| Basis Set                                          | comment                                            |
|====================================================|====================================================|
| GTO/CC-PV5Z                                        |                                                    |
+----------------------------------------------------+----------------------------------------------------+
| GTO/CC-PV6Z                                        |                                                    |
+----------------------------------------------------+----------------------------------------------------+
| GTO/CC-PVDZ                                        |                                                    |
+----------------------------------------------------+----------------------------------------------------+
| GTO/CC-PVQZ                                        |                                                    |
+----------------------------------------------------+----------------------------------------------------+
| GTO/CC-PVTZ                                        |                                                    |
+----------------------------------------------------+----------------------------------------------------+
| GTO/CC-PWCVQZ                                      |                                                    |
+----------------------------------------------------+----------------------------------------------------+

GTO type basis sets can be used to calculate high-quality RPA and MP2
/double-hybrid energies as well as GW QP energies (MBPT based
methods), often in combination with complete basis set (CBS) limit
extrapolation of the form

   E_{\text{CBS}} = \frac{Y^3 E_{Y} - X^3 E_{X}}{Y^3-X^3}

where E_{Y} denotes an energy or QP energy calculated with the cc-pVYZ
basis set and E_{X} denotes an energy or QP energy calculated with the
cc-pVXZ basis set, and Y > X . Typically, an extrapolation from a cc-
pVTZ and a cc-pVQZ calculation will give a result of cc-pV5Z quality
at lower computational cost.

When used in conjunction with MBPT based methods, a highly accurate
auxiliary fit set is needed (Also see the recommendations in the MBPT
section). It is recommended to generate the auxiliary fit sets
directly from products of basis functions to saturate all higher
angular momentum channels. See the RIHartreeFock documentation.


More Basis input options
========================

   Basis
      Folder string
      PerAtomType
         Core [None | Small | Medium | Large]
         File string
         Symbol string
         Type [SZ | DZ | DZP | TZP | TZ2P | QZ4P]
      End
      PerRegion
         Core [None | Small | Medium | Large]
         File string
         Region string
         Type [SZ | DZ | DZP | TZP | TZ2P | QZ4P]
      End
   End

"Basis"
   Type:
      Block

   Description:
      Definition of the basis set

   "Folder"
      Type:
         String

      Description:
         Path to a folder containing the basis set files. This can be
         used for special use-defined basis sets. Cannot be used in
         combination with 'Type'

   "PerAtomType"
      Type:
         Block

      Recurring:
         True

      Description:
         Defines the basis set for all atoms of a particular type.

      "Core"
         Type:
            Multiple Choice

         Options:
            [None, Small, Medium, Large]

         Description:
            Size of the frozen core.

      "File"
         Type:
            String

         Description:
            The path to the basis set file. The path can be absolute
            or relative to $AMSRESOURCES/Band. Specifying the path to
            the basis file explicitly overrides the automatic basis
            file selection via the Type and Core subkeys.

      "Symbol"
         Type:
            String

         Description:
            The symbol for which to define the basis set.

      "Type"
         Type:
            Multiple Choice

         Options:
            [SZ, DZ, DZP, TZP, TZ2P, QZ4P]

         Description:
            The basis sets to be used.

   "PerRegion"
      Type:
         Block

      Recurring:
         True

      Description:
         Defines the basis set for all atoms in a region. If
         specified, this overwrites the values set with the Basis%Type
         and Basis%PerAtomType keywords for atoms in that region. Note
         that if this keyword is used multiple times, the chosen
         regions may not overlap.

      "Core"
         Type:
            Multiple Choice

         Default value:
            Large

         Options:
            [None, Small, Medium, Large]

         Description:
            Size of the frozen core.

      "File"
         Type:
            String

         Description:
            The path to the basis set file. The path can be absolute
            or relative to $AMSRESOURCES/Band. Specifying the path to
            the basis file explicitly overrides the automatic basis
            file selection via the Type and Core subkeys.

      "Region"
         Type:
            String

         Description:
            The identifier of the region for which to define the basis
            set. Note that this may also be a region expression, e.g.
            'myregion+myotherregion' (the union of two regions).

      "Type"
         Type:
            Multiple Choice

         Default value:
            DZ

         Options:
            [SZ, DZ, DZP, TZP, TZ2P, QZ4P]

         Description:
            The basis sets to be used.

See also: Example: Multiresolution, and Frozen core.


Confinement of basis functions
==============================

It is possible to alter the radial part of the basis functions in
order to make them more compact, which will in turn speeds up the
calculation.

   SoftConfinement
      Quality [Auto | Basic | Normal | Good | VeryGood | Excellent]
      Radius float
      Delta float
   End

"SoftConfinement"
   Type:
      Block

   Description:
      In order to make the basis functions more compact, the radial
      part of the basis functions is multiplied by a Fermi-Dirac (FD)
      function (this 'confinement' is done for efficiency and
      numerical stability reasons). A FD function goes from one to
      zero, controlled by two parameters. It has a value 0.5 at
      Radius, and the decay width is Delta.

   "Quality"
      Type:
         Multiple Choice

      Default value:
         Auto

      Options:
         [Auto, Basic, Normal, Good, VeryGood, Excellent]

      GUI name:
         Confinement

      Description:
         In order to make the basis functions more compact, the radial
         part of the basis functions is multiplied by a Fermi-Dirac
         (FD) function (this 'confinement' is done for efficiency and
         numerical stability reasons). A FD function goes from one to
         zero, controlled by two parameters. It has a value 0.5 at
         Radius, and the decay width is Delta.
         This key sets the two parameters 'Radius' and 'Delta'.
         Basic: Radius=7.0, Delta=0.7;                      Normal:
         Radius=10.0, Delta=1.0;                      Good:
         Radius=20.0, Delta=2.0;                      VeryGood and
         Excellent: no confinement at all.                      If
         'Auto', the quality defined in the 'NumericalQuality' will be
         used.

   "Radius"
      Type:
         Float

      Unit:
         Bohr

      Description:
         Explicitly specify the radius parameter of the Fermi-Dirac
         function.

   "Delta"
      Type:
         Float

      Unit:
         Bohr

      Description:
         Explicitly specify the delta parameter of the Fermi-Dirac
         function (if not specified, it will be 0.1*Radius).

* For geometry optimizations under pressure, "Basic" soft confinement
  is recommended.


Manually specifying AtomTypes (expert option)
=============================================

"AtomType (block-type)"
   (*Expert Option*) 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 n^th  type, which in turn has atoms at positions defined by
   the n^th  "Atoms" key.

      AtomType ElementSymbol
         Dirac ChemSym
            {option}
            ...
            shells cores
            shell_specification {occupation_number}
            ...
         End
         {BasisFunctions
            shell_specification STO_exponent
            ...
         End}
         FitFunctions
            shell_specification STO_exponent
            ...
         End
      END

   The argument *ElementSymbol* to "AtomType" is the symbol of the
   element that is referred to in the "Atoms" key block.

   "Dirac (block-type)"
      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 STO fit functions for the crystal
      calculation. The argument *ChemSym* of this option is the symbol
      of the element 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. 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 STO fit functions. For example NumericalFit 2
      means that the squares of all s,p, and d NOs will be used as STO
      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.

   "BasisFunctions (block-type)"
      Slater-type orbitals, specified by quantum numbers n,:math:*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 (i.e. the numerical atomic
      orbitals, see key Dirac).

   "FitFunctions (block-type)"
      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
            End
            BasisFunctions
               1s 1.7
               ...
            End
            FitFunctions
               1s 13.5
               2s 11.0
               ...
            End
         End

   "TestFunctions (block-type)"
      An optional subkey of the "AtomType" key block is
      "TestFunctions" which has 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. For the time being the l value is
      ignored. A possible application is to include a very tight
      function, to increase the accuracy near a nucleus.


Basis Set Superposition Error (BSSE)
====================================

The Ghost Atom feature enables the calculation of Basis Set
Superposition Errors (BSSE). Normally, if you want to know the bonding
energy of system A with system B you calculate three energies

1. E(A+B)

2. E(A)

3. E(B)

The bond energy is then E(A+B) - E(A) - E(B)

The BSSE correction is about the idea that we can also calculate E(A)
including basis functions from molecule B.

You can make a ghost atom by simply adding "Gh." in front of the
element name, for instance "Gh.H" for a ghost hydrogen , "Gh.C" for a
ghost Carbon atom.

You will get a better bonding energy, closer to the basis set limit by
calculating

E(A+B) - E(\text{A with B as ghost}) - E(\text{B with A as ghost})

The BSSE correction is

E(A) - E(\text{A with B as ghost}) + E(B) - E(\text{B with A as
ghost})

See also: Example: BSSE correction

[1] Computational details: Single Point calculation, 'Good'
    NumericalQuality, no frozen core, 7 k-points, XC functional:
    GGA:PBE. Calculation performed on a 24 cores compute node. 96
    atoms in the unit cell.


Alternative elements / Virtual crystal approximation
====================================================

It is possible to define an alternative nuclear charge for an element.
If a certain site in a crystal has, say, a 50% occupation of C (Z=6)
and a 50% occupation of B (Z=5) you can use one alternative atom with
Z=5.5

Example:

   Atoms
      Si 0.0 0.0 0.0
      C  0.0 0.0 0.0 nuclear_charge=5.5   ! this site has a mixture of 50% C and B
   End

In this example the basis set is taken from the C atom, but you could
equally well specify the B atom here.  (In fact any atom type can be
specified here, but why would you like to use an Au basis set for this
situation.). Defining such an average element is in the spirit of the
Virtual Crystal Approximation (VCA), however, the fractional nuclear
charge approach does not work well when for instance the fractional z
is near the value of a noble gas. For instance when mixing Si (Z=14)
and C(Z=8) atoms you may get near Ne (Z=10), and the corresponding
lattice will be way too diffuse.

If you want to perform a scan it can be useful to use the
ModifyAlternativeElement option

Example:

   System
      ModifyAlternativeElements true

      Atoms
          Si 0.0 0.0 0.0
          H  0.0 0.0 0.0 nuclear_charge=5.6   ! Element H is ignored and will be "rounded" to nearest atom (for the basis set) in this case C
      End

In band an alternative element works well with the frozen core
approximation, using a smaller or no core has little effect. The VCA
relies on defining an average pseudopotential (commonly used in plane
wave programs) and is not identical to the alternative element
approach (defining an average nuclear charge).
