ABINIT Configuration with UDTSET for Hydrogen Simulations

Introduction to ABINIT Dataset Management

ABINIT is a powerful density functional theory (DFT) software package widely used for electronic structure calculations. One of its most useful features is the ability to define multiple datasets within a single input file, allowing researchers to perform systematic studies efficiently. The udtset (unit dataset) feature provides a sophisticated mechanism for creating related datasets with systematic parameter variations.

Basic Dataset Configuration

The simplest form of dataset configuration in ABINIT uses the ndtset variable to specify the number of datasets to be executed sequentially. Consider the following basic example:

ndtset 2

acell 10 10 10
ecut 10

   natom1  2
  geoopt1  "bfgs"
   ntime1  10
  tolmxf1  5.0d-4
   xcart1  -0.7  0.0 0.0
            0.7  0.0 0.0
  toldff1  5.0d-5
   nband1   1

   natom2  1
  nsppol2  2
  occopt2  2
   nband2  1 1
     occ2  1.0  0.0
  toldfe2  1.0d-6
   xcart2  0.0 0.0 0.0
  spinat2  0.0 0.0 1.0

This configuration defines two distinct calculations:

1. Dataset 1: A geometry optimisation of an H₂ molecule using the BFGS algorithm
2. Dataset 2: A spin-polarised calculation of a single hydrogen atom

Common Parameters

Parameters without dataset indices apply to all datasets:

• acell 10 10 10: Defines the supercell dimensions (10 Bohr in each direction)
• ecut 10: Sets the plane-wave kinetic energy cut-off to 10 Hartree
• ntypat 1 and znucl 1: Specify one atomic species (hydrogen)
• kptopt 0 and nkpt 1: Use a single k-point (Gamma point)

Advanced Configuration with UDTSET

The udtset feature becomes particularly powerful when conducting convergence studies or parameter sweeps. The syntax udtset M N creates M × N datasets organised in a two-dimensional grid.

Energy Cut-off Convergence Study

The following configuration demonstrates an energy cut-off convergence study:

ndtset 12  udtset 6 2

acell 10 10 10
ecut:? 10    ecut+? 5

Here, udtset 6 2 creates 12 datasets (6 series × 2 types). The notation:

• ecut:? sets the initial energy cut-off value
• ecut+? specifies the increment between successive datasets

This produces calculations with energy cut-offs of 10, 15, 20, 25, 30, and 35 Hartree for both molecular and atomic hydrogen systems.

Unit Cell Size Variation

Another common convergence test involves varying the supercell size:

ndtset 12  udtset 6 2

acell:? 8 8 8  acell+? 2 2 2
ecut 10

This configuration:

• Starts with an 8×8×8 Bohr³ cell
• Increments each dimension by 2 Bohr for each series
• Creates cells of 8, 10, 12, 14, 16, and 18 Bohr per side

Combined Parameter Variation

More sophisticated studies can vary multiple parameters simultaneously:

ndtset 2  udtset 1 2

acell:? 16 16 16  acell+? 2 2 2
ecut 25

This simplified example creates two datasets with cell sizes of 16 and 18 Bohr, both using a higher energy cut-off of 25 Hartree.

Physical Systems Under Study

Hydrogen Molecule (H₂)

The molecular calculations (dataset type 1) simulate an H₂ molecule with:

• Initial atomic positions at ±0.7 Bohr along the x-axis
• Geometry optimisation using the BFGS algorithm
• Convergence criteria:
  • tolmxf 5.0d-4: Maximum force tolerance
  • toldff 5.0d-5: Force difference tolerance
• Single occupied band (nband 1)

Hydrogen Atom (H)

The atomic calculations (dataset type 2) represent a spin-polarised hydrogen atom:

• Centred at the origin
• Spin polarisation: nsppol 2 (separate up and down spin channels)
• Occupation: one electron in the spin-up channel
• Fixed occupation scheme: occopt 2
• Energy convergence: toldfe 1.0d-6 Hartree

Pseudopotential Considerations

The calculations employ norm-conserving pseudopotentials from the ABINIT pseudopotential library:

pp_dirpath "$ABI_PSPDIR"
pseudos "Psdj_nc_sr_04_pw_std_psp8/H.psp8"

An alternative configuration uses PBE exchange-correlation functional:

pseudos "Psdj_nc_sr_04_pbe_std_psp8/H.psp8"

The PSP8 format provides:

• Norm-conserving potentials
• Scalar-relativistic corrections
• Optimised for accuracy in DFT calculations

Convergence Parameters and Numerical Stability

SCF Convergence

The self-consistent field calculations use:

• nstep 10: Maximum of 10 SCF iterations
• diemac 2.0: Dielectric constant for convergence acceleration (reduced to 1.0 in some configurations for systems requiring more careful treatment)

Geometry Optimisation

For molecular systems:

• geoopt "bfgs": Broyden-Fletcher-Goldfarb-Shanno algorithm
• ntime 10: Maximum of 10 ionic steps
• tolmxf 5.0d-4: Maximum force tolerance for convergence

Practical Applications and Best Practices

Conducting Convergence Studies

When performing convergence tests:

1. Energy cut-off convergence: Vary ecut systematically whilst keeping the cell size fixed
2. Cell size convergence: Increase acell to eliminate spurious interactions between periodic images
3. Combined testing: Once individual convergence is achieved, verify results with both parameters optimised

Interpreting Results

For each dataset series:

• Monitor total energy convergence with respect to ecut
• Verify that forces approach zero for geometry optimisations
• Check that atomic systems show expected spin polarisation
• Ensure molecular bond lengths converge to physically reasonable values

Computational Efficiency

The UDTSET approach offers several advantages:

• Single input file for multiple related calculations
• Automatic parameter variation reduces human error
• Systematic organisation facilitates data analysis
• Efficient use of computational resources through sequential execution

Conclusion

ABINIT's dataset configuration system, particularly the UDTSET feature, provides a powerful framework for conducting systematic computational studies. By enabling efficient parameter sweeps and convergence testing within a single input file, researchers can explore the parameter space methodically whilst maintaining reproducibility and reducing setup overhead. The examples presented here demonstrate fundamental techniques applicable to more complex systems and calculations.

Understanding these configuration methods is essential for conducting rigorous computational studies and ensuring the reliability of DFT calculations in materials science and quantum chemistry research.

References

ABINIT Documentation. "Input Variables." ABINIT Official Documentation. link

Gonze, Xavier, et al. "The ABINIT Project: Impact, Environment and Recent Developments." Computer Physics Communications 248 (2020): 107042. link

Gonze, Xavier, et al. "Recent Developments in the ABINIT Software Package." Computer Physics Communications 205 (2016): 106-131. link