2.2 Defaults for chemical elements: species_defaults

FHI-aims requires exactly two input files, located in the same directory where a calculation is started: control.in and geometry.in. Both files can in principle be specified from scratch for every new calculation, using the keywords listed in Chapter 3. However, maintaining consistent central computational settings across a series of calculations greatly enhances the accuracy of any resulting energy differences (error cancellation).

In FHI-aims, the key parameters regarding computational accuracy are actually subkeywords of the species keyword of control.in, controlling the basis set, all integration grids, and the accuracy of the Hartree potential. These settings should of course not be retyped from scratch for every single calculation; on the other hand, they should remain obvious to the user, since these are the central handles to determine the accuracy and efficiency of a given calculation.

In FHI-aims, the pivotal parameters concerning computational accuracy are housed as subkeywords of the species keyword in the control.in file. This governs the basis set, all integration grids, and the Hartree potential accuracy. It is recommended to refrain from recreating these settings from scratch for each calculation to ensure user clarity and facilitate the optimal balance between accuracy and efficiency in each computation.

FHI-aims therefore provides preconstructed default definitions for the important subkeywords associated with different species (chemical elements) ranging from $Z$ =1-102 (H-Md). These can be found in the species_defaults subdirectory of the distribution, and are built for inclusion into a control.in file by simple copy-paste.

For all elements, FHI-aims offers three or four different levels of species_defaults:

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light : These are the go-to settings for fast prerelaxations, structure searches, etc. In our own work, no obvious geometry / convergence errors resulted from these settings, and we now recommend them for many household tasks. For “final” results (meV-level converged energy differences between large molecular structures etc.), any results from the light level should be verified with more accurate post-processing calculations, e.g. intermediate or, if needed, tight.
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intermediate : This level plays an important role for large and expensive calculations, especially for hybrid functionals. Intermediate settings use most of the numerical settings from tight, but includes basis functions between light and tight. The cost of hybrid functionals scales heavily with the number of basis functions found on a given atom. Full tight settings, which were designed with the much cheaper semilocal functionals in mind, can be prohibitively expensive for large structures and hybrid density functionals. Hybrid DFT results from intermediate settings are typically completely sufficient for production results, offering a cost-effective solution. Intermediate settings are available for elements 1-86 except for lanthanides; for the latter, tight settings are the current recommended choice beyond light.
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tight : The settings specified here are rather save regarding the integration grids, Hartree potential, and basis cutoff potentials, and are intended to provide meV-level accurate energy differences also for large structures. In the tight settings, the basis set level is set to tier 2 for the light elements 1-10, a modified tier 1 for the slightly heavier Al, Si, P, S, Cl (the first spdfgd radial functions are enabled by default), and tier 1 for all other elements. This reflects the fact that, for heavy elements, tier 1 is sufficient for tightly converged ground state properties in DFT-LDA/GGA, but for the light elements (H-Ne), tier 2 is, e.g., required for meV-level converged energy differences. For convergence purposes, the specification of the basis set itself (tier 1, tier 2, etc.) may still be decreased / increased as needed. Note that especially for hybrid functionals, tight can already be very expensive and specific reductions of the number of radial functions may still provide essentially converged results at a much more affordable cost (see intermediate settings).
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really_tight : Same basis sets (radial functions and cutoff radii) as in the tight settings, but for the other numerical aspects (grids, Hartree potential), settings that are strongly overconverged settings for most purposes. The idea is that really_tight can be used for very specific, manual convergence tests of the basis set and other settings – if really needed.
Note that the “tight” settings are intended to provide reliably accurate results for most DFT production purposes; and they are not cheap. The absolute total energies for tight and DFT are in practice converged to some tens of meV/atom for most elements. To go beyond, take the really_tight settings and increase the basis set or other numerical aspects step by step. (Radial function by radial function may often be a good strategy to go.) We emphasize that the really_tight settings should only ever be needed for individual, specific tests. They should not be needed for any standard production tasks unless you have seriously too much CPU time to spend.
Specific differences between tight and the unmodified really_tight settings: The basis_dep_cutoff keyword is set to zero, a prerequisite to approach the converged basis limit. Regarding the Hartree potential, l_hartree is set to 8, and the maximum number of angular grid points per radial integration shell is increased to 590.
Note that there can still be corner cases where you may want to test some numerical setting beyond really_tight. Mostly, these are custom scenarios or things beyond standard FHI-aims calculations of DFT total energies. Examples include: The confinement radius for surface work functions (should be checked), use of very extended or extremely tight Gaussian-type orbital basis functions (e.g., from very large Dunning-type basis sets – the density of the radial and angular grids should be checked), or RPA and MP2 calculations, which can need very different and often much larger basis sets (again, radial and angular grids should be checked).

The FHI-aims species defaults light, tight, intermediate, tight, and really_tight are shipped in two versions in the folder species_defaults:

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defaults_2010 (now legacy)
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defaults_2020

We recommend using the re-worked defaults_2020. The updates of the light, tight, and really_tight defaults compared to the defaults_2010 version stem from a careful analysis of the Delta-Code DFT (DCDFT) Test (71 solids). The updates should, thus, improve the accuracy of an element for the material class (insulator or metal) that is present in the DCDFT Test (e.g., the Be crystal is metallic in the test, but may be an ion for some other systems).

Further species default variants included in defaults_2020:

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light_spd: The former light species defaults of default_2010 for the elements 13-17, 31-35, and 49-53. These settings are of use for simulations, where the former defaults were sufficient and very light computational settings are needed (e.g. MD simulations).
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minimal+s : Cost-efficient, near-minimal basis set to overcome runtime limitations and memory issues for fast (pre-)relaxation, MD, large-scale simulations of bulk-like systems. The "minimal+s" species defaults are based on the "light" species defaults. Due to the small basis set overly long bond lengths stemming from the basis set incompleteness error (BSIE) have to be corrected with a linear attractive pairwise correction. These correction term correction for energies, forces and stresses are parametrized against basis-set converged calculations for Z=1-86 (excluding lanthanides) parametrized for use with PBE functional. The correction is automatically invoked in FHI-aims by using the "minimal+s" species default files (found in FHIaims $\backslash$ species $\_$ defaults $\backslash$ defaults $\_$ 2020 $\backslash$ minimal+s $\backslash$ ). Specifically, the "species $\_$ default $\_$ type minimal+s" keyword in these files enables the corrections on a per-element basis. For use with other functionals than PBE, we recommend to verify your results with the larger "light", "tight" basis sets or by re-parametrizing the correction. If you observe issues or want to share your experience contact keller@fhi-berlin.mpg.de. When using "minimal+s" species defaults in your calculation, please cite Elisabeth Keller’s reference.
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intermediate_gw, tight_gw and really_tight_gw: Same as the standard intermediate, tight and really_tight species defaults, except that the auxiliary basis set to describe the Coulomb operator has been enhanced for periodic $G W$ calculations. Periodic $G W$ calculations rely on the RI-LVL scheme [151] and can require a larger set of auxiliary basis functions. This is done by adding for_aux functions to the basis set which adds extra high angular momentum radial functions. For intermediate_gw, we add for_aux hydro 4 f 0.0 while for tight_gw and really_tight_gw we add for_aux hydro 4 f 0.0 and for_aux hydro 5 g 0.0.

A separate group of species defaults for light elements (H-Ar) is available especially for calculations involving explicitly correlated methods (methods other than semilocal and hybrid density functionals):

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NAO-VCC-nZ : NAO type basis sets for H-Ar by Igor Ying Zhang and coworkers [327]. These basis sets are constructed according to Dunning’s “correlation consistent” recipe. Their intended application is for methods that invoke the continuum of unoccupied orbitals explicitly, for instance MP2, RPA or $G W$ . Note that they were constructed for valence-only correlation (hence “VCC”, valence correlation consistent), i.e., they work best in frozen-core correlated approaches following a full s.c.f. cycle (core and valence) to generate the orbitals. While NAO-VCC-nZ can be used for “normal” density functional theory (LDA, GGA, or hybrid functionals), the normal “light”, “intermediate”, “tight” and “really_tight” species defaults are more effective in those cases. The advantage of NAO-VCC-nZ over GTO basis sets such as the Dunning “cc” basis sets is that with NAOs, both the behaviour near the nucleus as well as that for the tails of orbitals far away from atoms is much more physical. This means that we can use more efficient integration grids than for GTO basis sets to obtain systematic convergence of the unoccupied state space.

The NAO-J-n basis sets are designed for the calculation of indirect spin-spin coupling constants (J-couplings):

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NAO-J-n : The basis sets are available for most light elements from H to Cl. Since these are more expensive (tighter grids) than other basis sets, they should only be used for J-couplings. Even then, they should only be placed on atoms of interest, while cheaper basis sets can be used on other atoms. They are constructed by adding tight Gaussian orbitals to the NAO-VCC-nZ basis sets. In order to describe the Gaussian orbitals correctly near the nucleus, tighter grids than normally are required (with radial_multiplier 8 and l_hartree 8, among other parameters). Other stages of the calculation, such as geometry relaxation, should be performed with basis sets more suitable for the particular task (using, e.g., the default tight settings).

In addition, the species_defaults directory contains a few more sets of species defaults for special purposes. These can be found in the non-standard subdirectory and include:

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gaussian_tight_770 : Species defaults that allow to perform calculation with some standard published Gaussian-type orbital (GTO) basis sets for elements H-Ar (including basis sets due to Pople, Dunning, Ahlrichs and their coworkers). These species defaults are meant to allow for exact benchmarks against GTO codes such as NWChem. The other numerical settings (especially grids) are thus much tighter than needed for “normal” NAO-type calculations. Note that FHI-aims is not optimized for GTO basis sets. We recommend NAO-type basis sets, not GTO basis sets, for production calculations – NAO-type basis sets are much easier to handle with our techniques and give better accuracy at lower cost. That said – the grid settings in the gaussian_tight_770 species defaults are rather overconverged for benchmark purposes. One could create much more efficient species defaults for GTO basis sets – but GTOs still would not be as efficient as NAO basis sets (at the same level of accuracy).
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Tier2_aug2 : Example, pioneered by Jan Kloppenburg, of basis sets that merge FHI-aims’ tier2 basis sets with a very reduced set of Gaussian augmentation functions taken from Dunning’s augmented correlation-consistent basis sets. This prescription appears to provide a remarkably accurate but affordable foundation to compute neutral (optical) vertical molecular excitation energies by linear-response time-dependent density functional theory, as well as (thanks to Chi (Garnett) Liu) the Bethe-Salpeter Equation.
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light_194 : This is just an example of how to tune down the normal “light” basis sets of FHI-aims by reducing the integration grid even further. For things like fast molecular-dynamics type screening of many structures, this is a perfectly viable approach. Examples are provided for H-Ne. Obviously, do test the impact of such modifications for your own purposes.

Additionally, any standard Gaussian-type basis sets can be obtained in FHI-aims format from the basis set exchange, https://www.basissetexchange.org/ .

For calculations that involve the excited state spectrum directly (this includes $G W$ , MP2, or RPA, among others), the numerical settings from tight still perform rather well if a counterpoise correction is performed (i.e., for energy differences). Still, the basis set size and/or cutoff radii must be converged and carefully verified beyond the settings specified in tight.

To extrapolate the absolute total energy of methods which rely on the unoccupied state continuum explicitly, e.g., RPA or MP2, we recommend using the NAO-VCC-nZ basis sets. These basis sets are presently available for light elements (H-Ar). A popular completeness-basis-set extrapolation scheme is two-point extrapolation:

E[\infty]=\frac{E[n_{1}]n_{1}^{3}-E[n_{2}]n_{2}^{3}}{n_{1}^{3}-n_{2}^{3}}

where “n₁” and “n₂” are the indicies of NAO-VCC-nZ. This $1/n^{3}$ formula was originally proposed for the correlation energy, but was also used directly for the total energy.