ABINIT Calculations for Aluminium Systems

Zhengqing Wei

November 15, 2025

Published in Computational Physics

Abstract

This article presents a series of sophisticated ABINIT input files demonstrating multi-dataset calculation techniques for aluminium systems, including k-point convergence studies, smearing temperature optimisation, and structural relaxation across diverse crystallographic configurations from bulk FCC to extended slab geometries.

Keywords: ABINIT, DFT, Aluminium, Multi-Dataset, Convergence Study, Structural Relaxation

Overview

The provided input files showcase eight distinct ABINIT calculations that systematically explore various computational parameters and structural configurations for aluminium. These examples are invaluable for researchers seeking to understand convergence behaviour, optimise computational parameters, and investigate aluminium structures ranging from simple bulk systems to complex slab geometries.

Dataset 1: Basic Structural Optimisation

The first calculation demonstrates a fundamental structural optimisation for FCC aluminium using a basic computational setup:

acell 3*7.60
rprim  0.0  0.5  0.5
       0.5  0.0  0.5
       0.5  0.5  0.0

ntypat 1
znucl 13
pp_dirpath "$ABI_PSPDIR"
pseudos "Psdj_nc_sr_04_pw_std_psp8/Al.psp8"

natom 1
typat 1
xred
0.0  0.0  0.0

ecut  6.0

ngkpt 2 2 2
nshiftk 4
shiftk 0.5 0.5 0.5
       0.5 0.0 0.0
       0.0 0.5 0.0
       0.0 0.0 0.5

nstep 10
toldfe 1.0d-6

occopt 4
tsmear 0.05

optcell 1
geoopt  "bfgs"
ntime  10
dilatmx 1.05
ecutsm  0.5

Key Features

Unit Cell: FCC primitive cell with an initial lattice parameter of 7.60 Bohr
K-point Mesh: 2×2×2 Monkhorst-Pack grid with four symmetry-reducing shifts
Energy Cutoff: 6.0 Hartree (relatively low for testing purposes)
Structural Optimisation: Full cell optimisation (optcell 1) using the BFGS algorithm
Electronic Smearing: Fermi-Dirac smearing with 0.05 Hartree broadening

The calculation allows up to 5% volume change (dilatmx 1.05) and employs an energy smearing of 0.5 Hartree for the plane-wave basis set cutoff (ecutsm), which helps achieve smoother convergence during cell optimisation.

Dataset 2: K-Point Convergence Study

The second input file implements a systematic k-point convergence study across four different mesh densities:

ndtset 4
getwfk -1

acell 3*7.60
rprim  0.0  0.5  0.5
       0.5  0.0  0.5
       0.5  0.5  0.0

ntypat 1
znucl 13
pp_dirpath "$ABI_PSPDIR"
pseudos "Psdj_nc_sr_04_pw_std_psp8/Al.psp8"

natom 1
typat 1
xred
0.0  0.0  0.0

ecut  6.0

nshiftk 4
shiftk  0.5 0.5 0.5
        0.5 0.0 0.0
        0.0 0.5 0.0
        0.0 0.0 0.5

ngkpt1  2 2 2
ngkpt2  4 4 4
ngkpt3  6 6 6
ngkpt4  8 8 8

nstep 10
tolvrs 1.0d-14

occopt 4
tsmear 0.05

optcell 1
geoopt  "bfgs"
ntime  10
dilatmx 1.05
ecutsm  0.5

Analysis

This calculation employs ndtset 4 to define four sequential datasets with progressively denser k-point meshes (2×2×2, 4×4×4, 6×6×6, and 8×8×8). The getwfk -1 directive ensures that each dataset initialises its wavefunctions from the previous calculation, accelerating convergence.

The convergence criterion has been tightened to tolvrs 1.0d-14, demanding extremely precise results for reliable comparison between k-point densities. This systematic approach allows researchers to determine the optimal k-point mesh that balances computational cost with accuracy.

Dataset 3: Multi-Dimensional Parameter Study

The third calculation demonstrates ABINIT's powerful multi-dimensional dataset capabilities, combining k-point and smearing temperature variations:

ndtset 12  udtset 3 4
getwfk -1

acell 3*7.60
rprim  0.0  0.5  0.5
       0.5  0.0  0.5
       0.5  0.5  0.0

ntypat 1
znucl 13
pp_dirpath "$ABI_PSPDIR"
pseudos "Psdj_nc_sr_04_pw_std_psp8/Al.psp8"

natom 1
typat 1
xred
0.0  0.0  0.0

ecut  6.0

nshiftk 4
shiftk  0.5 0.5 0.5
        0.5 0.0 0.0
        0.0 0.5 0.0
        0.0 0.0 0.5

ngkpt1?  2 2 2
ngkpt2?  4 4 4
ngkpt3?  6 6 6

nstep 10
toldfe 1.0d-6

occopt 4

tsmear?1  0.01
tsmear?2  0.02
tsmear?3  0.03
tsmear?4  0.04

optcell 1
geoopt  "bfgs"
ntime  10
dilatmx 1.05
ecutsm  0.5

Understanding the Multi-Dimensional Syntax

The directive udtset 3 4 creates a 3×4 matrix of calculations (12 total datasets), where:

The first index (3) corresponds to k-point densities: ngkpt1?, ngkpt2?, ngkpt3?
The second index (4) corresponds to smearing temperatures: tsmear?1, tsmear?2, tsmear?3, tsmear?4

This generates all combinations, enabling comprehensive exploration of parameter space. Such systematic studies are essential for understanding the interplay between different computational parameters and their impact on final results.

Dataset 4: Hexagonal Aluminium Structure

The fourth calculation investigates aluminium in a hexagonal cell arrangement:

acell 3*7.5593333886E+00
rprim  0.5 -0.5  0.0
       0.5  0.5  0.0
       0.0  0.0  1.0
chkprim 0

ntypat 1
znucl 13
pp_dirpath "$ABI_PSPDIR"
pseudos "Psdj_nc_sr_04_pw_std_psp8/Al.psp8"

natom 2
typat 2*1
xred
0.0  0.0  0.0
0.5  0.5  0.5

ecut  6.0

ngkpt  4 4 4
nshiftk 2
shiftk  0.5 0.0 0.5
        0.0 0.5 0.5

nstep 10
toldfe 1.0d-6

occopt 4
tsmear 0.04

Structural Details

This configuration employs a hexagonal lattice (rprim defines a hexagonal basal plane) with two atoms per unit cell. The chkprim 0 directive disables the automatic primitive cell detection, allowing explicit control over the cell definition. The reduced k-point shifts reflect the hexagonal symmetry, with only two shift vectors needed rather than four.

Dataset 5: Slab Geometry with Relaxation

The fifth calculation introduces a slab geometry along the c-axis:

acell 3*7.5593333886E+00
rprim  0.5 -0.5  0.0
       0.5  0.5  0.0
       0.0  0.0  2.0

ntypat 1
znucl 13
pp_dirpath "$ABI_PSPDIR"
pseudos "Psdj_nc_sr_04_pw_std_psp8/Al.psp8"

natom 3
typat 3*1
xred
0.0  0.0  0.0
0.5  0.5  0.25
0.0  0.0  0.5

ecut  6.0

ngkpt  4 4 1
nshiftk 2
shiftk  0.5 0.0 0.0
        0.0 0.5 0.0

nstep 10
toldff 5.0d-5

occopt 4
tsmear 0.04

geoopt "bfgs"
tolmxf 5.0d-4
ntime 10

Slab-Specific Considerations

The c-lattice vector has been doubled (rprim third row: 0.0 0.0 2.0), creating an extended cell along the z-direction. The k-point mesh reflects the reduced periodicity with ngkpt 4 4 1, using only one k-point along the non-periodic direction.

The convergence criteria have been changed to force-based tolerances:

toldff 5.0d-5: Maximum force tolerance
tolmxf 5.0d-4: Maximum force component tolerance

These are more appropriate for structural relaxation than energy-based criteria, particularly for slab geometries where surface relaxation is significant.

Dataset 6: Variable c-Axis Study

The sixth calculation explores two different c-axis extensions:

ndtset 2

acell  3*7.5593333886E+00
rprim1 0.5 -0.5  0.0
       0.5  0.5  0.0
       0.0  0.0  2.5
rprim2 0.5 -0.5  0.0
       0.5  0.5  0.0
       0.0  0.0  3.0

ntypat 1
znucl 13
pp_dirpath "$ABI_PSPDIR"
pseudos "Psdj_nc_sr_04_pw_std_psp8/Al.psp8"

natom 3
typat 3*1
xcart
3*0.0
0.0  2*3.7796666943
2*0.0  7.5593333886

ecut  6.0

ngkpt  4 4 1
nshiftk 2
shiftk  0.5 0.0 0.0
        0.0 0.5 0.0

nstep 6
toldff 5.0d-5

occopt 4
tsmear 0.04

geoopt "bfgs"
tolmxf 5.0d-4
ntime 10

Coordinate Specification

This calculation uses Cartesian coordinates (xcart) rather than reduced coordinates (xred), providing explicit atomic positions in Bohr. The two datasets compare structures with c-axis lengths of 2.5 and 3.0 times the base lattice constant, useful for studying interlayer interactions or optimising slab thickness.

Dataset 7: Progressive Slab Thickness Study

The seventh calculation extends the systematic study to three different slab thicknesses with varying atom numbers:

ndtset 3

acell  3*7.5593333886E+00
rprim1 0.5 -0.5  0.0
       0.5  0.5  0.0
       0.0  0.0  2.5
rprim2 0.5 -0.5  0.0
       0.5  0.5  0.0
       0.0  0.0  3.0
rprim3 0.5 -0.5  0.0
       0.5  0.5  0.0
       0.0  0.0  3.5
natom1 3
natom2 4
natom3 5

ntypat 1
znucl 13
pp_dirpath "$ABI_PSPDIR"
pseudos "Psdj_nc_sr_04_pw_std_psp8/Al.psp8"

typat 1 1 1 1 1
xcart
3*0.0
0.0  2*3.7796666943
2*0.0  7.5593333886
0.0  3.7796666943  11.3390000829
2*0.0 15.1186667772
chksymtnons 0

ecut  6.0

iprcel 45

ngkpt  4 4 1
nshiftk 2
shiftk  0.5 0.0 0.0
        0.0 0.5 0.0

nstep 10
toldff 5.0d-5

occopt 4
tsmear 0.04

geoopt "bfgs"
tolmxf 5.0d-4
ntime 10

Advanced Features

This calculation introduces several important directives:

chksymtnons 0: Disables checking of non-symmorphic symmetry operations, necessary when symmetry might be broken by the slab geometry
iprcel 45: Activates ionic preconditioner for improved convergence during structural relaxation

The three datasets systematically increase both the c-axis length (2.5, 3.0, 3.5) and the number of atoms (3, 4, 5), allowing investigation of convergence with respect to slab thickness.

Dataset 8: Extended Slab Series

The final calculation extends the slab thickness study to even larger systems:

ndtset 3

acell  3*7.5593333886E+00
rprim1 0.5 -0.5  0.0
       0.5  0.5  0.0
       0.0  0.0  3.5
rprim2 0.5 -0.5  0.0
       0.5  0.5  0.0
       0.0  0.0  4.0
rprim3 0.5 -0.5  0.0
       0.5  0.5  0.0
       0.0  0.0  4.5
natom1 5
natom2 6
natom3 7

ntypat 1
znucl 13
pp_dirpath "$ABI_PSPDIR"
pseudos "Psdj_nc_sr_04_pw_std_psp8/Al.psp8"

typat 1 1 1 1 1 1 1
xcart
3*0.0
0.0  2*3.7796666943
2*0.0  7.5593333886
0.0  3.7796666943  11.3390000829
2*0.0 15.1186667772
0.0  3.7796666943  18.8983334715
2*0.0 22.6780001658
chksymtnons 0

ecut  6.0

iprcel 45

ngkpt  4 4 1
nshiftk 2
shiftk  0.5 0.0 0.0
        0.0 0.5 0.0

nstep 10
toldfe 1.0d-6

occopt 4
tsmear 0.04

Convergence Considerations

This final calculation explores slabs with 5, 6, and 7 atoms, corresponding to c-axis extensions of 3.5, 4.0, and 4.5 times the base lattice constant. The convergence criterion has been returned to energy-based (toldfe 1.0d-6) from force-based, which may be more appropriate for these larger systems where force convergence could be challenging.

The systematic progression through these calculations allows determination of the minimum slab thickness required for converged surface or interface properties, a critical consideration in surface science and thin film studies.

Computational Best Practices

Parameter Selection

The calculations demonstrate several important computational choices:

K-Point Sampling: Progressive refinement from 2×2×2 to 8×8×8 establishes convergence, whilst slab geometries appropriately reduce sampling along the non-periodic direction (4×4×1)
Smearing Temperature: Values ranging from 0.01 to 0.05 Hartree are explored, with 0.04 Hartree commonly used for final production runs
Energy Cutoff: The consistent use of 6.0 Hartree represents a modest cutoff suitable for initial testing; production calculations would typically require higher values (15-20 Hartree for norm-conserving pseudopotentials)
Convergence Criteria: Appropriate selection between energy-based (toldfe, tolvrs) and force-based (toldff, tolmxf) criteria depending on calculation type

Multi-Dataset Strategy

The examples showcase ABINIT's powerful multi-dataset capabilities:

Sequential Datasets (getwfk -1): Each calculation initialises from the previous, improving efficiency
Multi-Dimensional Studies (udtset): Comprehensive parameter space exploration with minimal input complexity
Dataset-Specific Parameters: Variables can be specified per dataset (e.g., ngkpt1, rprim2) or globally

Practical Applications

These calculation templates are applicable to numerous research scenarios:

Convergence Studies: Establishing computational parameters for production runs
Surface Science: Investigating aluminium surface properties and reconstruction
Thin Film Physics: Studying quantum confinement effects in aluminium slabs
Interface Studies: Examining aluminium interfaces with vacuum or other materials
Method Validation: Benchmarking computational approaches against experimental data

Conclusion

The presented ABINIT input files provide a comprehensive framework for investigating aluminium systems through density functional theory calculations. The systematic progression from simple bulk optimisation through multi-parameter convergence studies to complex slab geometries demonstrates best practices in computational materials science.

Researchers can adapt these templates for their specific applications, adjusting parameters such as energy cutoff, k-point density, and convergence criteria based on required accuracy and available computational resources. The multi-dataset approach significantly enhances efficiency, enabling comprehensive studies whilst minimising manual intervention and data management complexity.

For further exploration of ABINIT capabilities and advanced features, researchers are encouraged to consult the official ABINIT documentation and tutorial resources.