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

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='runnervmeorf1', release='6.17.0-1010-azure', version='#10~24.04.1-Ubuntu SMP Fri Mar  6 22:00:57 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 2.4.3  scipy 1.17.1  h5py 3.16.0
Date: Wed Apr 22 12:34:00 2026
PySCF version 2.13.0
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:         3.29
tot grids = 33704
******** <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/tmp1kfq05th
max_memory 4000 MB (current use 610 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 0x7f898871a480>
grids dens level: 3
symmetrized grids: False
atomic radii adjust function: <function treutler_atomic_radii_adjust at 0x7f898871a3e0>
small_rho_cutoff = 0
Set gradient conv threshold to 3.16228e-05
Initial guess from minao.
init E= -76.2374175146669
  HOMO = -0.432688651711709  LUMO = -0.000586538415666027
cycle= 1 E= -76.2119597507852  delta_E= 0.0255  |g|= 0.754  |ddm|= 1.39
  HOMO = -0.0801446473734124  LUMO = 0.0738512196126857
cycle= 2 E= -76.0527933910275  delta_E= 0.159  |g|= 1.18  |ddm|= 1.34
  HOMO = -0.27308385717684  LUMO = 0.0310070473965167
cycle= 3 E= -76.3222362339212  delta_E= -0.269  |g|= 0.0274  |ddm|= 0.892
  HOMO = -0.268311629053107  LUMO = 0.0426599500044653
cycle= 4 E= -76.3223972522677  delta_E= -0.000161  |g|= 0.00519  |ddm|= 0.0171
  HOMO = -0.269282490560605  LUMO = 0.0426209039049517
cycle= 5 E= -76.3224012361862  delta_E= -3.98e-06  |g|= 0.000995  |ddm|= 0.0029
  HOMO = -0.269349032469923  LUMO = 0.0426066145034896
cycle= 6 E= -76.3224014309015  delta_E= -1.95e-07  |g|= 2.74e-05  |ddm|= 0.000635
  HOMO = -0.26935828589043  LUMO = 0.0426082034985567
cycle= 7 E= -76.3224014663473  delta_E= -3.54e-08  |g|= 1.87e-06  |ddm|= 3.58e-05
  HOMO = -0.269357663128986  LUMO = 0.0426082691989151
cycle= 8 E= -76.3224014602246  delta_E= 6.12e-09  |g|= 1.6e-07  |ddm|= 1.68e-06
  HOMO = -0.269357642386849  LUMO = 0.042608248525795
cycle= 9 E= -76.3224014569607  delta_E= 3.26e-09  |g|= 8.97e-09  |ddm|= 1.28e-07
  HOMO = -0.269357641987692  LUMO = 0.042608246722283
cycle= 10 E= -76.322401454916  delta_E= 2.04e-09  |g|= 6.84e-09  |ddm|= 7.34e-09
  HOMO = -0.269357643067548  LUMO = 0.0426082472220597
cycle= 11 E= -76.3224014551914  delta_E= -2.75e-10  |g|= 3.81e-09  |ddm|= 5.92e-09
  HOMO = -0.269357643205061  LUMO = 0.0426082478755903
Extra cycle  E= -76.3224014555722  delta_E= -3.81e-10  |g|= 5.9e-09  |ddm|= 6.15e-09
converged SCF energy = -76.3224014555722
Dipole moment(X, Y, Z, Debye):  0.00000, -0.00000, -1.98636
Total energy: -2076.838328 eV
Total energy: -76.322401 Hartree

Overwritten attributes  post_kernel pre_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}
<skala.ase.calculator.Skala object at 0x7f895ee12270>

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 12:34:41    -2076.839069        0.393157
LBFGSLineSearch:    1 12:34:53    -2076.841931        0.220730
LBFGSLineSearch:    2 12:35:17    -2076.844634        0.155733
LBFGSLineSearch:    3 12:35:27    -2076.844883        0.020197
LBFGSLineSearch:    4 12:35:37    -2076.844888        0.000616
Optimization completed in 4 steps
Initial energy: -2076.839069 eV
Final energy:   -2076.844888 eV
Energy change:  -0.005819 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

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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