Using Skala with the Atomic Simulation Environment (ASE)

Using Skala with the Atomic Simulation Environment (ASE)#

This tutorial provides a comprehensive overview of how to use the Skala neural network-based exchange-correlation functional with the Atomic Simulation Environment (ASE). The Skala functional is available as an ASE calculator, enabling accurate and scalable density functional theory calculations on molecular systems.

import numpy as np
from ase.build import molecule
from ase.optimize import LBFGSLineSearch as Opt
from ase.units import Hartree

from skala.ase import Skala

Basic Calculator Setup#

We can create the Skala calculator and set options like the basis set and density fitting when constructing the calculator. The calculator supports several key parameters:

xc: Exchange-correlation functional (default: “skala”)
basis: Basis set for the calculation (e.g., “def2-svp”, “def2-tzvp”)
with_density_fit: Enable density fitting for faster calculations
with_dftd3: Include DFT-D3 dispersion correction (default: True)
verbose: Control output verbosity (0-4)
with_retry: Enable retry mechanism for SCF convergence (default: True)
ks_config: Additional configuration options for the KS solver (e.g., convergence criteria)

# Create a water molecule
atoms = molecule("H2O")

# Set up the Skala calculator with specific parameters
atoms.calc = Skala(xc="skala-1.1", basis="def2-svp", verbose=4)

# Display the calculator parameters
print("Calculator parameters:")
for key, value in atoms.calc.parameters.items():
    print(f"  {key}: {value}")

Calculator parameters:
  xc: skala-1.1
  basis: def2-svp
  with_density_fit: False
  auxbasis: None
  with_newton: False
  with_dftd3: True
  with_retry: True
  charge: None
  multiplicity: None
  verbose: 4
  ks_config: None
  device: cpu

Energy Calculations#

Calculations can be performed by requesting properties from the atoms object, which is connected to the calculator. For example, we can calculate the total energy of a water molecule. The energy is returned in eV (ASE’s default energy unit):

# Calculate the total energy
energy_eV = atoms.get_potential_energy()  # eV
energy_Hartree = energy_eV / Hartree  # Convert to Hartree

print(f"Total energy: {energy_eV:.6f} eV")
print(f"Total energy: {energy_Hartree:.6f} Hartree")

System: uname_result(system='Linux', node='runnervmvrwv9', release='6.17.0-1020-azure', version='#20~24.04.1-Ubuntu SMP Fri Jun 19 20:09:14 UTC 2026', machine='x86_64')  Threads 2
Python 3.12.13 | packaged by conda-forge | (main, Mar  5 2026, 16:50:00) [GCC 14.3.0]
numpy 2.4.6  scipy 1.18.0  h5py 3.16.0
Date: Thu Jul 23 13:10:24 2026
PySCF version 2.13.1
PySCF path  /home/runner/micromamba/envs/skala/lib/python3.12/site-packages/pyscf

[CONFIG] conf_file None
[INPUT] verbose = 4
[INPUT] num. atoms = 3
[INPUT] num. electrons = 10
[INPUT] charge = 0
[INPUT] spin (= nelec alpha-beta = 2S) = 0
[INPUT] symmetry False subgroup None
[INPUT] Mole.unit = Angstrom
[INPUT] Symbol           X                Y                Z      unit          X                Y                Z       unit  Magmom
[INPUT]  1 O      0.000000000000   0.000000000000   0.119262000000 AA    0.000000000000   0.000000000000   0.225372517068 Bohr   0.0
[INPUT]  2 H      0.000000000000   0.763239000000  -0.477047000000 AA    0.000000000000   1.442312677587  -0.901488178545 Bohr   0.0
[INPUT]  3 H      0.000000000000  -0.763239000000  -0.477047000000 AA    0.000000000000  -1.442312677587  -0.901488178545 Bohr   0.0

nuclear repulsion = 9.08829376913928
number of shells = 12
number of NR pGTOs = 38
number of NR cGTOs = 24
basis = def2-svp
ecp = {}
CPU time:         2.66
tot grids = 33698
******** <class 'skala.pyscf.dft.SkalaRKS'> ********
method = SkalaRKS
initial guess = minao
damping factor = 0
level_shift factor = 0
DIIS = <class 'pyscf.scf.diis.CDIIS'>
diis_start_cycle = 1
diis_space = 8
diis_damp = 0
SCF conv_tol = 1e-09
SCF conv_tol_grad = None
SCF max_cycles = 50
direct_scf = True
direct_scf_tol = 1e-13
chkfile to save SCF result = /tmp/tmpb9vr98v5
max_memory 4000 MB (current use 551 MB)
XC library libxc version None
    None
XC functionals = custom
radial grids: 
    Treutler-Ahlrichs [JCP 102, 346 (1995); DOI:10.1063/1.469408] (M4) radial grids
becke partition: Becke, JCP 88, 2547 (1988); DOI:10.1063/1.454033
pruning grids: <function nwchem_prune at 0x7f02b0957740>
grids dens level: 3
symmetrized grids: False
atomic radii adjust function: <function treutler_atomic_radii_adjust at 0x7f02b09576a0>
small_rho_cutoff = 0
Set gradient conv threshold to 3.16228e-05
Initial guess from minao.
init E= -76.2374175395917
  HOMO = -0.43268865126937  LUMO = -0.000586538738660547
cycle= 1 E= -76.2119597648381  delta_E= 0.0255  |g|= 0.754  |ddm|= 1.39
  HOMO = -0.0801446479219061  LUMO = 0.073851232075846
cycle= 2 E= -76.0527934036559  delta_E= 0.159  |g|= 1.18  |ddm|= 1.34
  HOMO = -0.273083856436625  LUMO = 0.031007055474698
cycle= 3 E= -76.3222362355425  delta_E= -0.269  |g|= 0.0274  |ddm|= 0.892
  HOMO = -0.268311627914315  LUMO = 0.0426599515203869
cycle= 4 E= -76.3223972725541  delta_E= -0.000161  |g|= 0.00519  |ddm|= 0.0171
  HOMO = -0.269282489648297  LUMO = 0.042620899998131
cycle= 5 E= -76.32240124569  delta_E= -3.97e-06  |g|= 0.000995  |ddm|= 0.0029
  HOMO = -0.269349034096664  LUMO = 0.0426066137034877
cycle= 6 E= -76.3224014363668  delta_E= -1.91e-07  |g|= 2.74e-05  |ddm|= 0.000635
  HOMO = -0.269358286995716  LUMO = 0.0426082070663831
cycle= 7 E= -76.3224014645974  delta_E= -2.82e-08  |g|= 1.87e-06  |ddm|= 3.58e-05
  HOMO = -0.2693576604654  LUMO = 0.0426082693264234
cycle= 8 E= -76.3224014594619  delta_E= 5.14e-09  |g|= 1.6e-07  |ddm|= 1.68e-06
  HOMO = -0.269357639865017  LUMO = 0.0426082514651571
cycle= 9 E= -76.3224014574065  delta_E= 2.06e-09  |g|= 9.08e-09  |ddm|= 1.31e-07
  HOMO = -0.269357639976573  LUMO = 0.0426082503037319
cycle= 10 E= -76.3224014576005  delta_E= -1.94e-10  |g|= 9.12e-09  |ddm|= 5.75e-09
  HOMO = -0.269357642897981  LUMO = 0.0426082516238386
Extra cycle  E= -76.3224014564044  delta_E= 1.2e-09  |g|= 9.78e-09  |ddm|= 1.08e-08
converged SCF energy = -76.3224014564044
Dipole moment(X, Y, Z, Debye): -0.00000, -0.00000, -1.98636
Total energy: -2076.838328 eV
Total energy: -76.322401 Hartree

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Overwritten attributes  pre_kernel post_kernel  of <class 'skala.pyscf.dft.SkalaRKS'>

Updating Calculator Parameters#

To update the calculator parameters, we can use the set method. For example, we can activate density fitting to speed up the calculation and make the output less verbose. Note that changing certain parameters will reset the calculator and clear previous results.

# Update calculator settings
changed_params = atoms.calc.set(
    with_density_fit=True,
    verbose=0,
    auxbasis="def2-universal-jkfit",
    ks_config={"conv_tol": 1e-6},
)
print(changed_params)
print(f"Changed parameters: {changed_params}")

# Show current parameters
print("\nCurrent calculator parameters:")
for key, value in atoms.calc.parameters.items():
    print(f"  {key}: {value}")

print(atoms.calc)

{'with_density_fit': True, 'verbose': 0, 'auxbasis': 'def2-universal-jkfit', 'ks_config': {'conv_tol': 1e-06}}
Changed parameters: {'with_density_fit': True, 'verbose': 0, 'auxbasis': 'def2-universal-jkfit', 'ks_config': {'conv_tol': 1e-06}}

Current calculator parameters:
  xc: skala-1.1
  basis: def2-svp
  with_density_fit: True
  auxbasis: def2-universal-jkfit
  with_newton: False
  with_dftd3: True
  with_retry: True
  charge: None
  multiplicity: None
  verbose: 0
  ks_config: {'conv_tol': 1e-06}
  device: cpu
<skala.ase.calculator.Skala object at 0x7f028d1ca810>

Force Calculations#

We can continue to use the calculator for further calculations, such as computing the forces on the atoms. Since we changed the settings above, the calculator was reset and all previous results have been cleared. Requesting the forces will trigger a new calculation with the updated parameters.

# Calculate forces
forces = atoms.get_forces()  # eV/Å

print("Forces on atoms (eV/Å):")
for i, (symbol, force) in enumerate(
    zip(atoms.get_chemical_symbols(), forces, strict=True)
):
    print(
        f"  Atom {i + 1} ({symbol}): [{force[0]:8.4f}, {force[1]:8.4f}, {force[2]:8.4f}]"
    )

# Calculate maximum force component
max_force = np.max(np.abs(forces))
print(f"\nMaximum force component: {max_force:.4f} eV/Å")

Forces on atoms (eV/Å):
  Atom 1 (O): [  0.0000,   0.0000,  -0.0771]
  Atom 2 (H): [  0.0000,  -0.3913,   0.0385]
  Atom 3 (H): [ -0.0000,   0.3913,   0.0385]

Maximum force component: 0.3913 eV/Å

Geometry Optimization#

To use the calculator for geometry optimization or molecular dynamics simulations, you can use the optimize or dynamics modules from ASE. Here we’ll perform a geometry optimization to find the minimum energy structure:

# Store initial geometry for comparison
initial_positions = atoms.positions.copy()
initial_energy = atoms.get_potential_energy()

# Set up and run geometry optimization
opt = Opt(atoms, trajectory="water_opt.traj")
opt.run(fmax=0.01)  # Optimize until forces are below 0.01 eV/Å

# Show optimization results
final_energy = atoms.get_potential_energy()
final_forces = atoms.get_forces()
max_final_force = np.max(np.abs(final_forces))

print(f"Optimization completed in {opt.get_number_of_steps()} steps")
print(f"Initial energy: {initial_energy:.6f} eV")
print(f"Final energy:   {final_energy:.6f} eV")
print(f"Energy change:  {final_energy - initial_energy:.6f} eV")
print(f"Maximum final force: {max_final_force:.4f} eV/Å")

                 Step     Time          Energy          fmax
LBFGSLineSearch:    0 13:10:56    -2076.839069        0.393157
LBFGSLineSearch:    1 13:11:06    -2076.841931        0.220730
LBFGSLineSearch:    2 13:11:25    -2076.844634        0.155919
LBFGSLineSearch:    3 13:11:34    -2076.844883        0.020198
LBFGSLineSearch:    4 13:11:42    -2076.844889        0.000619
Optimization completed in 4 steps
Initial energy: -2076.839069 eV
Final energy:   -2076.844889 eV
Energy change:  -0.005820 eV
Maximum final force: 0.0006 eV/Å

Dipole Moment Calculations#

The Skala calculator also supports dipole moment calculations, which are useful for understanding molecular polarity:

# Calculate dipole moment
dipole = atoms.get_dipole_moment()  # Debye

print(
    f"Dipole moment vector (Debye): [{dipole[0]:8.4f}, {dipole[1]:8.4f}, {dipole[2]:8.4f}]"
)
print(f"Dipole moment magnitude: {np.linalg.norm(dipole):.4f} Debye")

Dipole moment vector (Debye): [ -0.0000,   0.0000,  -0.4190]
Dipole moment magnitude: 0.4190 Debye

Working with Different Molecules and Basis Sets#

Let’s explore how to work with different molecular systems and basis sets. Here we’ll calculate properties for methane (CH₄) using a larger basis set:

# Create a methane molecule
atoms = molecule("CH4")

# Set up calculator with a larger basis set and density fitting
atoms.calc = Skala(
    xc="skala-1.1",
    basis="def2-tzvp",  # Triple-zeta basis set
    with_density_fit=True,  # Enable density fitting for efficiency
    auxbasis="def2-universal-jkfit",
    with_dftd3=True,  # Include dispersion correction
    verbose=1,
)

print("Methane molecule:")
print(f"Chemical formula: {atoms.get_chemical_formula()}")
print(f"Number of atoms: {len(atoms)}")

# Calculate properties
energy = atoms.get_potential_energy()
forces = atoms.get_forces()
max_force = np.max(np.abs(forces))

print("\nCalculation results:")
print(f"Total energy: {energy:.6f} eV")
print(f"Maximum force: {max_force:.6f} eV/Å")

Methane molecule:
Chemical formula: CH4
Number of atoms: 5

Calculation results:
Total energy: -1102.336883 eV
Maximum force: 0.060181 eV/Å

Using Skala on GPU#

In case you have access to a compatible GPU, you can enable GPU acceleration by setting the device parameter to "cuda" when initializing the calculator. This can significantly speed up calculations for larger systems.

calc = Skala(
    xc="skala-1.1",
    basis="def2-tzvp",
    with_density_fit=True,
    auxbasis="def2-universal-jkfit",
    device="cuda",  # Enable GPU acceleration
)

The device can be changed at any time, causing the calculator to reset and use the new device for subsequent calculations.

calc.set(device="cpu")

{'device': 'cpu'}

Summary#

This tutorial covered the essential features of the Skala ASE calculator:

Setting up the calculator with various parameters
Calculating energies, forces, and dipole moments
Updating calculator parameters dynamically
Performing geometry optimizations
Working with different molecules and basis sets